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Beyond Advanced · Structure of Atom

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1
An α\alpha-particle of kinetic energy 6.0 MeV6.0\ \text{MeV} is fired head-on at a 12C{}^{12}\text{C} nucleus that is free and initially at rest (it is not held by any lattice). Take the masses in the ratio of their mass numbers, 4:124:12, and treat both as point charges, α\alpha with charge +2e+2e and carbon with +6e+6e. Use e24πε0=1.44 MeV fm\dfrac{e^{2}}{4\pi\varepsilon_0}=1.44\ \text{MeV fm} and ignore nuclear forces and radiation. Find the smallest distance between the centres of the two nuclei during the encounter, in fm.
Not attempted
Your answer: —
Correct answer: 3.84
2
Consider the six species 1840Ar{}^{40}_{18}\text{Ar}, 1940K+{}^{40}_{19}\text{K}^{+}, 2040Ca2+{}^{40}_{20}\text{Ca}^{2+}, 1939K{}^{39}_{19}\text{K}, 1737Cl−{}^{37}_{17}\text{Cl}^{-} and 1838Ar{}^{38}_{18}\text{Ar}. Which of the following statements is/are correct? (Count protons, neutrons and electrons for each species before deciding.)
Not attempted
A
40Ar{}^{40}\text{Ar}, 40K+{}^{40}\text{K}^{+} and 40Ca2+{}^{40}\text{Ca}^{2+} are mutually isobars and also mutually isoelectronic, but they are not mutually isotones.
B
39K{}^{39}\text{K}, 37Cl−{}^{37}\text{Cl}^{-} and 40Ca2+{}^{40}\text{Ca}^{2+} are mutually isotones although no two of them have the same number of electrons except 37Cl−{}^{37}\text{Cl}^{-} and 40Ca2+{}^{40}\text{Ca}^{2+}.
C
37Cl−{}^{37}\text{Cl}^{-} and 38Ar{}^{38}\text{Ar} are both isoelectronic and isotones, and yet they are not isobars.
D
40K+{}^{40}\text{K}^{+} and 39K{}^{39}\text{K} are isotopes of potassium and, as isotopes, they contain the same number of electrons.
3
In a discharge-tube experiment four kinds of positive ions, 1H+{}^{1}\text{H}^{+}, 2H+{}^{2}\text{H}^{+}, 4He2+{}^{4}\text{He}^{2+} and 4He+{}^{4}\text{He}^{+}, are all produced with the same kinetic energy and enter a uniform magnetic field perpendicular to their velocity. Take the mass of each ion proportional to its mass number. Let rr denote the radius of the circular path of an ion. Which of the following correctly describes the radii?
Not attempted
A
r(H+)<r(2H+)=r(He2+)<r(He+)r(\text{H}^{+})<r({}^{2}\text{H}^{+})=r(\text{He}^{2+})<r(\text{He}^{+})
B
r(He2+)<r(H+)<r(2H+)<r(He+)r(\text{He}^{2+})<r(\text{H}^{+})<r({}^{2}\text{H}^{+})<r(\text{He}^{+})
C
r(H+)=r(He2+)<r(2H+)<r(He+)r(\text{H}^{+})=r(\text{He}^{2+})<r({}^{2}\text{H}^{+})<r(\text{He}^{+})
D
r(H+)=r(2H+)<r(He2+)<r(He+)r(\text{H}^{+})=r({}^{2}\text{H}^{+})<r(\text{He}^{2+})<r(\text{He}^{+})
4
A gold foil of thickness 2.88 μm2.88\ \mu\text{m} is made of layers of atoms. Treat every atom as a sphere of radius 0.144 nm0.144\ \text{nm} (diameter 0.288 nm0.288\ \text{nm}), centred on a nucleus of radius 7.0 fm7.0\ \text{fm}. The layers are stacked so that each layer is shifted sideways at random relative to the others, so the nuclei in different layers never shadow each other, and the foil is thin enough that an α\alpha-particle meets each layer once and the chance of hitting a nucleus in any single layer is tiny. An α\alpha-particle is counted as 'scattered through a large angle' only if it passes within the geometric cross-section of a nucleus. Out of 1.0×1071.0\times10^{7} α\alpha-particles incident normally, about how many are scattered through a large angle?
Not attempted
gold foil: N atomic layers, each shifted at random⋮α
A
about 2.4×1022.4\times10^{2}
B
about 4.7×1024.7\times10^{2}
C
about 2.4×10−22.4\times10^{-2}
D
about 9.5×1029.5\times10^{2}
5
An α\alpha-particle of kinetic energy 7.0 MeV7.0\ \text{MeV} approaches a fixed tin nucleus (Z=50Z=50) with an impact parameter b=12.0 fmb=12.0\ \text{fm} (the perpendicular distance between the nucleus and the initial line of motion, as drawn). Use e24πε0=1.44 MeV fm\dfrac{e^{2}}{4\pi\varepsilon_0}=1.44\ \text{MeV fm}, point charges, and ignore nuclear forces and radiation. Find the distance of closest approach in fm.
Not attempted
nucleus (fixed)αb
Your answer: —
Correct answer: 26.09
6
Which of the following statements is/are correct?
Not attempted
A
Inside a Thomson atom (a uniform sphere of positive charge with electrons embedded) the electrostatic force on an α\alpha-particle is largest when it passes through the centre of the sphere.
B
If a nucleus of radius 10−15 m10^{-15}\ \text{m} sits in an atom of radius 10−10 m10^{-10}\ \text{m}, the nucleus occupies about 10−1510^{-15} of the atom's volume, although it blocks about 10−1010^{-10} of the atom's cross-sectional area.
C
The charge-to-mass ratio of cathode rays does not depend on the gas in the tube or on the cathode metal, whereas that of anode rays does depend on the gas.
D
A classical electron going round a nucleus at the Bohr radius 0.529 A˚0.529\ \text{\AA} with speed 2.18×106 m s−12.18\times10^{6}\ \text{m s}^{-1} would complete about 6.6×10136.6\times10^{13} revolutions per second.
7
In Rutherford scattering by a fixed nucleus, let dd be the distance of closest approach of an α\alpha-particle fired head-on, d=2Ze24πε0Kd=\dfrac{2Ze^{2}}{4\pi\varepsilon_0K}. For an impact parameter bb the deflection angle θ\theta obeys tan⁡θ2=d2b\tan\dfrac{\theta}{2}=\dfrac{d}{2b}. Which graph shows how the deflection angle depends on b/db/d?
Not attempted
A
Graph 2
b/dθ0.51290°180°
B
Graph 3
b/dθ0.51290°180°
C
Graph 4
b/dθ0.51290°180°
D
Graph 1
b/dθ0.51290°180°
8
A mass spectrometer is used to study the molecule CH2BrCl\text{CH}_2\text{BrCl} in the gas phase. Assume the only isotopes present are 12C{}^{12}\text{C} and 13C{}^{13}\text{C}, 1H{}^{1}\text{H} and 2H{}^{2}\text{H} (D), 79Br{}^{79}\text{Br} and 81Br{}^{81}\text{Br}, 35Cl{}^{35}\text{Cl} and 37Cl{}^{37}\text{Cl}, and take every isotopic mass equal to its mass number. The molecular-ion peaks are recorded for singly charged molecular ions. How many different molecular-ion peaks (different masses) appear?
Not attempted
A
66
B
88
C
1616
D
1212
9
In Chadwick's analysis of the radiation from beryllium bombarded by α\alpha-particles, neutral particles of unknown mass mm (in atomic mass units) hit hydrogen nuclei (mass 1 u1\ \text{u}) and nitrogen nuclei (mass 14 u14\ \text{u}). The maximum recoil speeds, from head-on elastic collisions with the same incident particles, were 3.3×107 m s−13.3\times10^{7}\ \text{m s}^{-1} for hydrogen and 4.7×106 m s−14.7\times10^{6}\ \text{m s}^{-1} for nitrogen. Use only these data. The mass of the neutral particle is closest to
Not attempted
A
0.99 u0.99\ \text{u}
B
1.16 u1.16\ \text{u}
C
1.50 u1.50\ \text{u}
D
2.30 u2.30\ \text{u}
10
Match the entries of List-I with List-II. List-IList-IIP)1840Ar & 2040Ca2+1)isotopes and isoelectronicQ)1735Cl− & 1737Cl−2)isobars and isoelectronicR)1939K+ & 1737Cl−3)isotones and isoelectronicS)614C & 816O4)isotones only, not isoelectronic5)isobars only, not isoelectronic\begin{array}{ll} \textbf{List-I} & \textbf{List-II} \\ \text{P)} {}^{40}_{18}\text{Ar}\ \&\ {}^{40}_{20}\text{Ca}^{2+} & \text{1)} \text{isotopes and isoelectronic} \\ \text{Q)} {}^{35}_{17}\text{Cl}^{-}\ \&\ {}^{37}_{17}\text{Cl}^{-} & \text{2)} \text{isobars and isoelectronic} \\ \text{R)} {}^{39}_{19}\text{K}^{+}\ \&\ {}^{37}_{17}\text{Cl}^{-} & \text{3)} \text{isotones and isoelectronic} \\ \text{S)} {}^{14}_{6}\text{C}\ \&\ {}^{16}_{8}\text{O} & \text{4)} \text{isotones only, not isoelectronic} \\ & \text{5)} \text{isobars only, not isoelectronic} \end{array}
Not attempted
A
P-1, Q-2, R-4, S-3
B
P-2, Q-3, R-1, S-5
C
P-5, Q-1, R-4, S-3
D
P-2, Q-1, R-3, S-4
11
In a photocell the emitter has work function 2.30 eV2.30\ \text{eV} and the collector (a different metal, connected to the emitter through a variable voltage source as shown) has work function 4.50 eV4.50\ \text{eV}. Light of wavelength 400 nm400\ \text{nm} falls only on the emitter. Use hc=1240 eV nmhc=1240\ \text{eV nm}, assume the plates are clean, parallel and in vacuum, and ignore space charge. The source is set to make the collector positive with respect to the emitter (an accelerating voltage). What is the smallest accelerating voltage, in volts, for which a photocurrent is detected?
Not attempted
emitterφ = 2.30 eVcollectorφ = 4.50 eV400 nmvariable source
Your answer: —
Correct answer: 1.4
12
The figure shows the maximum kinetic energy of photoelectrons against photon energy for two metals X and Y. Metal X has work function 2.0 eV2.0\ \text{eV} and metal Y has 3.2 eV3.2\ \text{eV}. Use hc=1240 eV nmhc=1240\ \text{eV nm}. Let VXV_X and VYV_Y be their stopping potentials for the same monochromatic light. Which of the following statements is/are correct?
Not attempted
hν (eV)K max (eV)12345−22XY
A
For any wavelength below 387.5 nm387.5\ \text{nm}, VX−VY=1.2 VV_X-V_Y=1.2\ \text{V}, whatever the wavelength.
B
As the wavelength is reduced below 387.5 nm387.5\ \text{nm} the ratio VX/VYV_X/V_Y decreases steadily towards 11, and at 300 nm300\ \text{nm} it equals 2.292.29.
C
Reducing the wavelength from 300 nm300\ \text{nm} to 150 nm150\ \text{nm} makes the stopping potential of each metal increase by the same factor.
D
Doubling the intensity of the 300 nm300\ \text{nm} light doubles VXV_X, because twice as many photons are absorbed.
13
A photocell with a fixed emitter of work function 2.0 eV2.0\ \text{eV} is illuminated in turn by three monochromatic sources and the photocurrent is plotted against the applied voltage (negative values mean a retarding voltage), as shown for curves 1, 2 and 3. Sources 2 and 3 deliver the same power to the emitter. Use hc=1240 eV nmhc=1240\ \text{eV nm}. Quantum yield means the fraction of incident photons that eject an electron. Which statement is correct?
Not attempted
V (volt)I (μA)−2−10124123
A
Source 3 has the higher frequency, and its quantum yield is 43\dfrac{4}{3} times that for source 2.
B
Source 3 has the higher frequency, and its quantum yield is 34\dfrac{3}{4} times that for source 2.
C
Source 3 has higher intensity than source 2, because its stopping potential is larger; sources 1 and 2 have different frequencies.
D
Source 3 has the lower frequency, because its curve cuts the voltage axis at a more negative value; its quantum yield equals that of source 2.
14
A metal has a threshold wavelength of 600 nm600\ \text{nm}. It is illuminated simultaneously by two collimated beams: beam A of wavelength 700 nm700\ \text{nm} and intensity 1.0 kW m−21.0\ \text{kW m}^{-2}, and beam B of wavelength 450 nm450\ \text{nm} and intensity 1.0 W m−21.0\ \text{W m}^{-2}. Intensities are low enough that two-photon absorption is negligible. Use hc=1240 eV nmhc=1240\ \text{eV nm}. The maximum kinetic energy of the emitted photoelectrons is
Not attempted
metal (threshold 600 nm)A: 700 nm, 1.0 kW/m²B: 450 nm, 1.0 W/m²
A
2.46 eV2.46\ \text{eV}
B
zero, because the intense 700 nm700\ \text{nm} beam delivers far more energy than the weak beam
C
0.69 eV0.69\ \text{eV}
D
0.98 eV0.98\ \text{eV}
15
Light of wavelength 250 nm250\ \text{nm} falls on a large flat metal plate of work function 2.30 eV2.30\ \text{eV}. A uniform magnetic field B=1.2 mTB=1.2\ \text{mT} exists in the vacuum above the plate, parallel to its surface. Photoelectrons are emitted in all directions into the half-space above the plate (directions arbitrarily close to the surface included). Use hc=1240 eV nmhc=1240\ \text{eV nm}, me=9.1×10−31 kgm_e=9.1\times10^{-31}\ \text{kg}, e=1.602×10−19 Ce=1.602\times10^{-19}\ \text{C}, and ignore electric fields and collisions. What is the greatest height above the plate that any photoelectron can reach, in mm?
Not attempted
Your answer: —
Correct answer: 9.16
16
For a certain metal and monochromatic light of wavelength λ\lambda, the maximum kinetic energy of the photoelectrons is KK. When the wavelength is reduced by 25%25\% (to 0.75λ0.75\lambda) the maximum kinetic energy becomes exactly 3K3K. If instead the wavelength is halved (to λ/2\lambda/2), by what factor does the maximum kinetic energy increase over KK?
Not attempted
Your answer: —
Correct answer: 7
17
Use h=6.626×10−34 J sh=6.626\times10^{-34}\ \text{J s}, c=3.0×108 m s−1c=3.0\times10^{8}\ \text{m s}^{-1} and hc=1240 eV nmhc=1240\ \text{eV nm}. Which of the following statements is/are correct?
Not attempted
A
A photon whose wavenumber is 2.5×106 m−12.5\times10^{6}\ \text{m}^{-1} has an energy of 3.10 eV3.10\ \text{eV}.
B
Two lamps radiate equal power, one in violet light (400 nm400\ \text{nm}) and one in red light (700 nm700\ \text{nm}). The violet lamp emits 1.751.75 times as many photons per second as the red lamp.
C
A 100 W100\ \text{W} lamp that turns 5%5\% of its power into light of wavelength 600 nm600\ \text{nm} emits about 1.5×10191.5\times10^{19} photons per second.
D
Light of wavelength 560 nm560\ \text{nm} and intensity 1.0 W m−21.0\ \text{W m}^{-2} falling normally and entirely absorbed on an area of 1.0 cm21.0\ \text{cm}^{2} delivers about 2.8×10142.8\times10^{14} photons per second.
18
White light from a hot filament passes through a cool (room-temperature) sample of atomic hydrogen gas and then through a spectrograph covering 200 nm200\ \text{nm} to 800 nm800\ \text{nm}. Take the Rydberg constant 1.097×107 m−11.097\times10^{7}\ \text{m}^{-1}. What is seen in the transmitted spectrum?
Not attempted
A
Dark lines at 656656, 486486, 434434 and 410 nm410\ \text{nm}, at the positions of the hydrogen Balmer emission lines.
B
Bright lines at 656656, 486486, 434434 and 410 nm410\ \text{nm} on a continuous background, because the gas re-emits the absorbed light.
C
Dark lines at 122122, 103103, 97 nm97\ \text{nm} in the range of the spectrograph, since these are the strongest absorption lines.
D
No dark lines in this range: the lines that atoms in the ground state can absorb lie in the ultraviolet below 122 nm122\ \text{nm}.
19
In a photoelectric experiment the emitter has work function 1.01.0 eV and is lit by photons of energy 3.03.0 eV, giving stopping potential V0=2.0V_0=2.0 V and saturation current Is=10 μAI_s=10\ \mu\text{A}. In every case below only the stated change is made, and the fraction of incident photons that eject an electron stays the same. Match each change in List-I with the resulting values in List-II. List-IList-IIP)Light intensity is doubled at the same frequency1)V0=2.0 V, Is=20 μAQ)Wavelength is halved at the same power2)V0=5.0 V, Is=5 μAR)The emitter is replaced by one of work function 2.0 eV, same light3)V0=1.0 V, Is=10 μAS)Frequency and power are both doubled4)V0=5.0 V, Is=10 μA5)V0=4.0 V, Is=10 μA\begin{array}{ll} \textbf{List-I} & \textbf{List-II} \\ \text{P)} \text{Light intensity is doubled at the same frequency} & \text{1)} V_0=2.0\ \text{V},\ I_s=20\ \mu\text{A} \\ \text{Q)} \text{Wavelength is halved at the same power} & \text{2)} V_0=5.0\ \text{V},\ I_s=5\ \mu\text{A} \\ \text{R)} \text{The emitter is replaced by one of work function 2.0 eV, same light} & \text{3)} V_0=1.0\ \text{V},\ I_s=10\ \mu\text{A} \\ \text{S)} \text{Frequency and power are both doubled} & \text{4)} V_0=5.0\ \text{V},\ I_s=10\ \mu\text{A} \\ & \text{5)} V_0=4.0\ \text{V},\ I_s=10\ \mu\text{A} \end{array}
Not attempted
A
P-1, Q-4, R-3, S-2
B
P-1, Q-2, R-3, S-4
C
P-2, Q-1, R-5, S-4
D
P-5, Q-2, R-1, S-3
20
Three lamps of equal power emit monochromatic light of wavelengths 400 nm400\ \text{nm}, 500 nm500\ \text{nm} and 650 nm650\ \text{nm}. Each in turn illuminates the same metal surface (work function 2.2 eV2.2\ \text{eV}) with all its power absorbed, and the voltage is large enough to collect every emitted electron. The fraction of photons that eject an electron is the same, 0.0100.010, for every photon that has enough energy to do so. Use hc=1240 eV nmhc=1240\ \text{eV nm}. The saturation photocurrents I400:I500:I650I_{400}:I_{500}:I_{650} are in the ratio
Not attempted
A
5:4:05:4:0
B
1:1:11:1:1
C
4:5:04:5:0
D
1:1:01:1:0
21
A perfectly reflecting thin mirror of mass 12 mg12\ \text{mg} hangs freely in space, initially at rest. A laser beam of power 3.7 mW3.7\ \text{mW} and wavelength 650 nm650\ \text{nm} hits it normally and is reflected straight back. All of the beam strikes the mirror, and the mirror moves slowly enough to ignore Doppler shifts. Take c=3.0×108 m s−1c=3.0\times10^{8}\ \text{m s}^{-1}. How long, in minutes, does the beam take to give the mirror a speed of 5.0 mm s−15.0\ \text{mm s}^{-1}?
Not attempted
Your answer: —
Correct answer: 40.54
22
A sample of He+\text{He}^{+} ions is excited so that electrons occupy every level up to n=8n=8, and all the 2828 possible transitions n2→n1n_2\to n_1 (with 8≥n2>n1≥18\ge n_2>n_1\ge1) occur. Ignore the reduced-mass correction, so that wavenumbers are exactly RHZ2(1n12−1n22)R_H Z^{2}\left(\dfrac{1}{n_1^{2}}-\dfrac{1}{n_2^{2}}\right). How many of these 2828 lines have a wavelength exactly equal to that of some line in the emission spectrum of atomic hydrogen? (A hydrogen line may come from any upper level m2>m1m_2>m_1, no matter how large.)
Not attempted
HHe⁺n=1n=2n=1n=2n=3n=3…8n=4…8energy levels to the same scale
Your answer: —
Correct answer: 7
23
An electron in the n=2n=2 level of a Li2+\text{Li}^{2+} ion stays there for a mean time of 1.0×10−8 s1.0\times10^{-8}\ \text{s} before dropping to a lower level. Use the Bohr model with vn=2.18×106Zn m s−1v_n=2.18\times10^{6}\dfrac{Z}{n}\ \text{m s}^{-1} and rn=0.529n2Z A˚r_n=0.529\dfrac{n^{2}}{Z}\ \text{\AA}. How many revolutions does the electron make in this time? Give the answer in units of 10710^{7} revolutions.
Not attempted
Your answer: —
Correct answer: 7.38
24
In the Bohr model, the revolving electron of a hydrogen-like species acts as a current loop and produces a magnetic field at the nucleus. Let B1B_1 be this field for the electron of Li2+\text{Li}^{2+} in its n=3n=3 orbit and B2B_2 the corresponding field for a hydrogen atom with its electron in the n=2n=2 orbit. The ratio B1/B2B_1/B_2 is
Not attempted
A
329\dfrac{32}{9}
B
83\dfrac{8}{3}
C
22
D
163\dfrac{16}{3}
25
A gas of hydrogen atoms in their ground state is studied. Excitation energies of the atom are 13.6(1−1n2) eV13.6\left(1-\dfrac{1}{n^{2}}\right)\ \text{eV} for the level nn. Treat a collision with an electron as able to transfer any energy up to the electron's kinetic energy, and note that a photon is absorbed only if its whole energy is used. Consider the following statements.
Not attempted
E (eV)n=1 0.00n=2 10.20n=3 12.09n=4 12.75n=5, 6, … 13.06 to 13.60excitation energy above ground state
A
Bombarding the gas with electrons of kinetic energy 12.5 eV12.5\ \text{eV} makes the gas emit exactly three different spectral lines.
B
Irradiating the same gas with photons of energy 12.5 eV12.5\ \text{eV} also makes it emit exactly three different spectral lines.
C
Bombarding the gas with electrons of kinetic energy 13.0 eV13.0\ \text{eV} makes it emit exactly ten different spectral lines.
D
An atom that has just been excited to n=2n=2 by absorbing a 10.2 eV10.2\ \text{eV} photon can absorb a second photon of the same energy, and is then ionised, the electron leaving with a kinetic energy of 6.8 eV6.8\ \text{eV}.
26
A hydrogen atom of mass 1.67×10−27 kg1.67\times10^{-27}\ \text{kg}, initially at rest, drops from n=2n=2 to n=1n=1 and emits the Lyman-α\alpha photon. Take the energy of the photon as 10.2 eV10.2\ \text{eV} with 1 eV=1.6×10−19 J1\ \text{eV}=1.6\times10^{-19}\ \text{J} and c=3.0×108 m s−1c=3.0\times10^{8}\ \text{m s}^{-1}. The atom recoils non-relativistically. The speed of the atom after the emission is closest to
Not attempted
A
3.26 m s−13.26\ \text{m s}^{-1}
B
1.63 m s−11.63\ \text{m s}^{-1}
C
6.51 m s−16.51\ \text{m s}^{-1}
D
1.4×104 m s−11.4\times10^{4}\ \text{m s}^{-1}
27
Using RH=1.097×107 m−1R_H=1.097\times10^{7}\ \text{m}^{-1}, consider the series of the hydrogen spectrum with lower level n1=1,2,3,4,5n_1=1,2,3,4,5 (Lyman, Balmer, Paschen, Brackett, Pfund). Each series stretches from its longest-wavelength line (n2=n1+1n_2=n_1+1) to its series limit (n2→∞n_2\to\infty). Which of the following statements is/are correct?
Not attempted
A
The Balmer and Paschen series overlap in wavelength.
B
The Paschen and Brackett series overlap in wavelength.
C
Exactly five lines of the Balmer series lie in the visible range 400400-750 nm750\ \text{nm}.
D
Every line of the Pfund series has a longer wavelength than every line of the Brackett series.
28
Hydrogen atoms in the n=3n=3 level drop directly to n=1n=1, and the emitted radiation falls on a metal of work function 3.8 eV3.8\ \text{eV}. The fastest photoelectrons are collected. Use En=−13.6/n2 eVE_n=-13.6/n^{2}\ \text{eV}, h=6.626×10−34 J sh=6.626\times10^{-34}\ \text{J s}, me=9.1×10−31 kgm_e=9.1\times10^{-31}\ \text{kg} and 1 eV=1.602×10−19 J1\ \text{eV}=1.602\times10^{-19}\ \text{J}. Find the de Broglie wavelength of these fastest photoelectrons, in A˚\text{\AA}.
Not attempted
Your answer: —
Correct answer: 4.26
29
The figure shows four emission transitions in a hydrogen atom (the levels are labelled by nn and are not drawn to scale). Each arrow runs from the upper level to the lower level of its transition. In which order do the wavelengths of the emitted photons increase (shortest first)?
Not attempted
n=1n=2n=3n=4n=5n=6PQRSlevels not drawn to scale
A
S<Q<P<RS<Q<P<R
B
R<P<S<QR<P<S<Q
C
Q<S<P<RQ<S<P<R
D
S<Q<R<PS<Q<R<P
30
Consider the electron of He+\text{He}^{+} in its n=2n=2 orbit, of Li2+\text{Li}^{2+} in its n=3n=3 orbit and of Be3+\text{Be}^{3+} in its n=4n=4 orbit, according to the Bohr model. Which of the following statements is/are correct?
Not attempted
A
The three electrons have the same total energy, the same speed and the same de Broglie wavelength.
B
Their periods of revolution are in the ratio 4:9:164:9:16.
C
The magnetic fields they produce at their own nuclei are in the ratio 14:19:116\dfrac{1}{4}:\dfrac{1}{9}:\dfrac{1}{16}.
D
The three orbits have radii in the ratio 4:9:164:9:16.
31
Match each description in List-I with the number in List-II. Hydrogen atoms are in the Bohr model; use the usual selection of all downward transitions. List-IList-IIP)A sample of H atoms is excited to n = 5; total number of different spectral lines1)3Q)Sample excited to n = 5; number of those lines that end on n = 22)5R)Sample excited to n = 6; number of lines ending on a level with n at least 33)6S)One single atom excited to n = 6; greatest number of photons it can emit on returning to n = 14)105)15\begin{array}{ll} \textbf{List-I} & \textbf{List-II} \\ \text{P)} \text{A sample of H atoms is excited to n = 5; total number of different spectral lines} & \text{1)} \text{3} \\ \text{Q)} \text{Sample excited to n = 5; number of those lines that end on n = 2} & \text{2)} \text{5} \\ \text{R)} \text{Sample excited to n = 6; number of lines ending on a level with n at least 3} & \text{3)} \text{6} \\ \text{S)} \text{One single atom excited to n = 6; greatest number of photons it can emit on returning to n = 1} & \text{4)} \text{10} \\ & \text{5)} \text{15} \end{array}
Not attempted
A
P-4, Q-2, R-3, S-1
B
P-4, Q-1, R-3, S-2
C
P-5, Q-1, R-2, S-3
D
P-3, Q-4, R-1, S-2
32
Helium ions He+\text{He}^{+} in their ground state are bombarded by electrons. The energy levels are En=−54.4n2 eVE_n=-\dfrac{54.4}{n^{2}}\ \text{eV}, an electron can transfer any energy up to its kinetic energy to an ion, and you may use RH=1.097×107 m−1R_H=1.097\times10^{7}\ \text{m}^{-1} for the wavelengths. What is the smallest kinetic energy of the electrons, in eV, for which the ions emit any light in the visible range (400400-750 nm750\ \text{nm})?
Not attempted
Your answer: —
Correct answer: 51
33
He+\text{He}^{+} ions are excited to n=6n=6 and all 1515 possible transitions between levels 11 to 66 take place. The emitted photons are shone on hydrogen atoms in their ground state. A hydrogen atom absorbs a photon either if its energy is exactly equal to an excitation energy of the atom (13.6(1−1/m2) eV13.6(1-1/m^{2})\ \text{eV}, m≥2m\ge2), or if it is at least the ionisation energy 13.6 eV13.6\ \text{eV}. Use En=−13.6Z2/n2 eVE_n=-13.6Z^{2}/n^{2}\ \text{eV} and ignore reduced-mass corrections. For how many of the 1515 transitions of He+\text{He}^{+} can the emitted photon be absorbed by a ground-state hydrogen atom?
Not attempted
Your answer: —
Correct answer: 7
34
Which of the following statements comparing the Bohr model with the quantum mechanical (orbital) model of the hydrogen atom is/are correct? (The orbital angular momentum in the quantum mechanical model is l(l+1)h2π\sqrt{l(l+1)}\dfrac{h}{2\pi}.)
Not attempted
A
For the ground state, Bohr's model gives an orbital angular momentum h2π\dfrac{h}{2\pi}, whereas the 1s1s electron of quantum mechanics has zero orbital angular momentum.
B
For n=2n=2 the Bohr value 2h2π\dfrac{2h}{2\pi} is larger than the quantum mechanical value 2h2π\sqrt{2}\dfrac{h}{2\pi} of a 2p2p electron.
C
In the quantum mechanical model the 2s2s and 2p2p levels of the hydrogen atom have different energies because their orbital angular momenta differ.
D
Both models give the same energy expression En=−13.6/n2 eVE_n=-13.6/n^{2}\ \text{eV} for the hydrogen atom.
35
A discharge contains hydrogen atoms and He+\text{He}^{+} ions. A line in the infrared emitted by He+\text{He}^{+} has exactly the same wavelength as the first line of the Brackett series of hydrogen (the 5→45\to4 transition). Ignore reduced-mass corrections. The He+\text{He}^{+} transition is
Not attempted
A
n=5→n=4n=5\to n=4
B
n=7→n=6n=7\to n=6
C
n=9→n=8n=9\to n=8
D
n=10→n=8n=10\to n=8
36
A beam of electrons accelerated from rest through 150 V travels in vacuum and strikes the flat surface of a crystal at an angle of incidence of 60∘60^{\circ} (measured from the normal). Inside the crystal each electron sits in an average potential that is 15 V15\ \text{V} lower (more attractive) than in vacuum, so its kinetic energy increases by 15 eV15\ \text{eV} on entering. The surface is flat, so only the component of momentum normal to it changes. Ignore reflection. Find the angle of refraction of the electron wave inside the crystal, in degrees.
Not attempted
crystal (inner potential +15 V)vacuume⁻ beam?
Your answer: —
Correct answer: 55.66
37
A proton is to be given a de Broglie wavelength exactly equal to the circumference of the second Bohr orbit of He+\text{He}^{+}. Use rn=0.529n2Z A˚r_n=0.529\dfrac{n^{2}}{Z}\ \text{\AA}, h=6.626×10−34 J sh=6.626\times10^{-34}\ \text{J s}, mp=1.673×10−27 kgm_p=1.673\times10^{-27}\ \text{kg}, 1 eV=1.602×10−19 J1\ \text{eV}=1.602\times10^{-19}\ \text{J}. The kinetic energy the proton must have is closest to
Not attempted
He⁺electron wave in the n = 2 orbit
A
7.41 meV7.41\ \text{meV}
B
0.46 meV0.46\ \text{meV}
C
1.85 meV1.85\ \text{meV}
D
3.41 eV3.41\ \text{eV}
38
A beam of electrons accelerated from rest through 100 V100\ \text{V} passes through a long narrow slit of width a=1.2 μma=1.2\ \mu\text{m}. Use the uncertainty principle in the form Δy⋅Δpy=h4π\Delta y\cdot\Delta p_y=\dfrac{h}{4\pi} with Δy=a\Delta y=a, and take the angular spread of the emerging beam as θ≈Δpyp\theta\approx\dfrac{\Delta p_y}{p}. Use h=6.626×10−34 J sh=6.626\times10^{-34}\ \text{J s}, me=9.1×10−31 kgm_e=9.1\times10^{-31}\ \text{kg}, e=1.602×10−19 Ce=1.602\times10^{-19}\ \text{C}. Find θ\theta in microradians.
Not attempted
screen with slitelectronsaspread ±θ
Your answer: —
Correct answer: 8.14
39
Use h=6.626×10−34 J sh=6.626\times10^{-34}\ \text{J s} and me=9.1×10−31 kgm_e=9.1\times10^{-31}\ \text{kg}, with the uncertainty relations Δx Δp≥h4π\Delta x\,\Delta p\ge\dfrac{h}{4\pi} and ΔE Δt≥h4π\Delta E\,\Delta t\ge\dfrac{h}{4\pi}. Which of the following statements is/are correct?
Not attempted
A
An electron known to be within 0.529 A˚0.529\ \text{\AA} of a nucleus has an uncertainty in speed of at least about 1.1×106 m s−11.1\times10^{6}\ \text{m s}^{-1}, comparable to its Bohr speed.
B
An electron moving at about 2.2×106 m s−12.2\times10^{6}\ \text{m s}^{-1} whose speed is known to ±1%\pm1\% cannot be located to better than about 2.6×10−9 m2.6\times10^{-9}\ \text{m}, which is about fifty atomic radii.
C
An excited state with a lifetime of 1.0×10−8 s1.0\times10^{-8}\ \text{s} has an energy uncertainty of at least about 5.3×10−27 J5.3\times10^{-27}\ \text{J}.
D
With a better position-measuring instrument one could, in principle, make the product Δx Δp\Delta x\,\Delta p for an electron smaller than h4π\dfrac{h}{4\pi}.
40
A photon and an electron have the same wavelength, 1.00 A˚1.00\ \text{\AA}. Take h=6.626×10−34 J sh=6.626\times10^{-34}\ \text{J s}, c=3.0×108 m s−1c=3.0\times10^{8}\ \text{m s}^{-1} and me=9.1×10−31 kgm_e=9.1\times10^{-31}\ \text{kg} (the electron is non-relativistic). The ratio of the energy of the photon to the kinetic energy of the electron is closest to
Not attempted
A
8282
B
4141
C
165165
D
1.01.0
41
A crude quantum estimate of the kinetic energy of an electron in a He+\text{He}^{+} ion takes the position uncertainty equal to the first Bohr radius of He+\text{He}^{+} (r1=0.529/2 A˚r_1=0.529/2\ \text{\AA}), the momentum uncertainty from Δx Δp=h4π\Delta x\,\Delta p=\dfrac{h}{4\pi}, and the kinetic energy as (Δp)22m\dfrac{(\Delta p)^{2}}{2m}. Use h=6.626×10−34 J sh=6.626\times10^{-34}\ \text{J s}, me=9.1×10−31 kgm_e=9.1\times10^{-31}\ \text{kg} and 1 eV=1.602×10−19 J1\ \text{eV}=1.602\times10^{-19}\ \text{J}. What kinetic energy, in eV, does this estimate give?
Not attempted
Your answer: —
Correct answer: 13.63
42
The figure shows the standing de Broglie wave of the single electron of a Be3+\text{Be}^{3+} ion drawn around its stable Bohr orbit (the dashed circle marks the mean orbit; the wave is drawn with exaggerated amplitude, and an exact whole number of wavelengths fits round the orbit). Use rn=0.529n2Z A˚r_n=0.529\dfrac{n^{2}}{Z}\ \text{\AA} and En=−13.6Z2n2 eVE_n=-13.6\dfrac{Z^{2}}{n^{2}}\ \text{eV}. Which of the following statements is/are correct?
Not attempted
Be³⁺ nucleus
A
The radius of the orbit is about 3.31 A˚3.31\ \text{\AA}.
B
The energy of the electron is about −8.70 eV-8.70\ \text{eV}.
C
The orbital angular momentum of the electron is 4h2π4\dfrac{h}{2\pi}.
D
The standing wave has exactly 55 nodes (points where it crosses the mean orbit) round the orbit.
43
A proton (mass mm, charge ee), a deuteron (mass 2m2m, charge ee) and an α\alpha-particle (mass 4m4m, charge 2e2e) are compared. Which of the following statements is/are correct?
Not attempted
A
If all three have the same speed, their de Broglie wavelengths are in the ratio 4:2:14:2:1.
B
If the proton and the α\alpha-particle have the same kinetic energy, the proton's wavelength is twice that of the α\alpha-particle.
C
If the deuteron and the α\alpha-particle are each accelerated from rest through the same potential difference, they acquire equal de Broglie wavelengths.
D
If the deuteron and the α\alpha-particle have the same kinetic energy, the wavelength of the deuteron is 2\sqrt{2} times that of the α\alpha-particle.
44
Match the entries of List-I with List-II. List-IList-IIP)An electron of kinetic energy 100 eV1)1.23 A˚Q)A proton with the same kinetic energy as that electron2)0.0286 A˚R)An alpha-particle with the same speed as that proton3)0.0101 A˚S)A deuteron with the same momentum as an alpha-particle accelerated through 100 V4)0.00716 A˚5)0.0143 A˚\begin{array}{ll} \textbf{List-I} & \textbf{List-II} \\ \text{P)} \text{An electron of kinetic energy 100 eV} & \text{1)} \text{1.23 Å} \\ \text{Q)} \text{A proton with the same kinetic energy as that electron} & \text{2)} \text{0.0286 Å} \\ \text{R)} \text{An alpha-particle with the same speed as that proton} & \text{3)} \text{0.0101 Å} \\ \text{S)} \text{A deuteron with the same momentum as an alpha-particle accelerated through 100 V} & \text{4)} \text{0.00716 Å} \\ & \text{5)} \text{0.0143 Å} \end{array}
Not attempted
A
P-1, Q-2, R-3, S-4
B
P-2, Q-1, R-4, S-3
C
P-1, Q-5, R-4, S-2
D
P-1, Q-2, R-4, S-3
45
Electrons accelerated through 54 V54\ \text{V} strike, along the normal, a single row of equally spaced atoms of spacing dd. A maximum of the scattered intensity of first order is found at 50∘50^{\circ} from the normal, as in the figure, on each side. The constructive condition for the row is dsin⁡φ=nλd\sin\varphi=n\lambda (n=1,2,…n=1,2,\ldots). Use λ=12.27V A˚\lambda=\dfrac{12.27}{\sqrt{V}}\ \text{\AA} with VV in volts. The voltage is now raised to 100 V100\ \text{V}. For the first-order maximum the new angle is closest to
Not attempted
e⁻1st-order max50°row of atoms, spacing d
A
37∘37^{\circ}, and no second-order maximum exists
B
34∘34^{\circ}, and no second-order maximum exists
C
27∘27^{\circ}, and a second-order maximum exists at 65∘65^{\circ}
D
34∘34^{\circ}, and a second-order maximum exists at 69∘69^{\circ}
46
A beam of neutrons has de Broglie wavelength 1.8 A˚1.8\ \text{\AA}. The neutrons are in thermal equilibrium with a moderator, so their average kinetic energy is 32kBT\dfrac{3}{2}k_BT (take the wavelength as that of a neutron of exactly this energy). Use h=6.626×10−34 J sh=6.626\times10^{-34}\ \text{J s}, mn=1.675×10−27 kgm_n=1.675\times10^{-27}\ \text{kg} and kB=1.38×10−23 J K−1k_B=1.38\times10^{-23}\ \text{J K}^{-1}. The temperature of the moderator is closest to
Not attempted
A
293 K293\ \text{K}
B
195 K195\ \text{K}
C
98 K98\ \text{K}
D
391 K391\ \text{K}
47
The n=3n=3 level of a hydrogen atom lives for about 1.5×10−8 s1.5\times10^{-8}\ \text{s} before emitting the red HαH_\alpha line (656 nm656\ \text{nm}). Take the lower level as sharp, use the minimum value in ΔE Δt=h4π\Delta E\,\Delta t=\dfrac{h}{4\pi}, and c=3.0×108 m s−1c=3.0\times10^{8}\ \text{m s}^{-1}. What is the corresponding minimum spread Δλ\Delta\lambda in the wavelength of the emitted line, in femtometres (1 fm=10−15 m1\ \text{fm}=10^{-15}\ \text{m})?
Not attempted
Your answer: —
Correct answer: 7.61
48
In the ground state of krypton (Z=36Z=36), how many electrons have a magnetic quantum number mlm_l and an azimuthal quantum number ll whose sum is zero, l+ml=0l+m_l=0?
Not attempted
Your answer: —
Correct answer: 16
49
Consider the ground state of a zinc atom (Z=30Z=30). Every occupied orbital is a separate orbital with its own nodal pattern; count the radial (spherical) nodes and the angular nodes (nodal planes or cones) of each occupied orbital, and add them up over all occupied orbitals of the atom. What is (total number of angular nodes) −- (total number of radial nodes)?
Not attempted
Your answer: —
Correct answer: 7
50
The figure shows the radial probability distribution 4πr2ψ24\pi r^{2}\psi^{2} of a single orbital of a hydrogen atom against rr in units of the Bohr radius a0a_0. The wave function of this orbital has two angular nodes (nodal surfaces that pass through the nucleus). The orbital is
Not attempted
r (a₀)4πr²ψ²O10203040
A
3d3d
B
5d5d
C
4p4p
D
4d4d
51
Which of the following statements about orbitals is/are correct?
Not attempted
A
The dz2d_{z^{2}} orbital has no nodal plane through the nucleus; its two angular nodes are conical surfaces, and it has a ring-shaped region of high density in the xyxy-plane.
B
The lobes of the dxyd_{xy} orbital point between the xx and yy axes, and its two nodal planes are the xzxz-plane and the yzyz-plane.
C
The 4dx2−y24d_{x^{2}-y^{2}} orbital has three nodal surfaces in all, of which exactly one is spherical.
D
The pxp_x orbital has a single nodal plane (the yzyz-plane), and the wave function has opposite signs on the two lobes although the probability density is the same on both sides.
52
Consider all possible electrons of the shell with principal quantum number n=4n=4 (all allowed values of ll, mlm_l and msm_s). Which of the following statements is/are correct?
Not attempted
A
The shell contains orbitals with seven different values of mlm_l.
B
The shell contains orbitals with sixteen different values of mlm_l.
C
Exactly 88 of the electrons that can occupy the shell have ml=0m_l=0.
D
Exactly 66 of the electrons that can occupy the shell have ml=+2m_l=+2.
53
The orbital angular momentum of the electron of a hydrogen atom has magnitude 12 h2π\sqrt{12}\,\dfrac{h}{2\pi}, and its orbital has two spherical (radial) nodes. The electron is in the
Not attempted
A
6f6f orbital
B
5f5f orbital
C
6d6d orbital
D
5g5g orbital
54
In the ground state of selenium (Z=34Z=34), how many electrons have n+l=5n+l=5 and spin quantum number ms=+12m_s=+\dfrac{1}{2}? Assume that, as in Hund's rule, every unpaired electron has ms=+12m_s=+\dfrac{1}{2}, and that in a pair one electron has each spin.
Not attempted
Your answer: —
Correct answer: 8
55
The energy of an electron in a one-electron species (hydrogen atom or hydrogen-like ion) depends on nn and the nuclear charge ZZ only. Which of the following pairs of orbitals have exactly the same energy?
Not attempted
A
the 3d3d orbital of He+\text{He}^{+} and the 2p2p orbital of H\text{H}
B
the 2s2s orbital of Li2+\text{Li}^{2+} and the 2s2s orbital of He+\text{He}^{+}
C
the 2p2p orbital of He+\text{He}^{+} and the 1s1s orbital of H\text{H}
D
the 3p3p orbital of Be3+\text{Be}^{3+} and the 2s2s orbital of Li2+\text{Li}^{2+}
56
Match each orbital of a one-electron atom in List-I, given by its principal quantum number nn and its orbital angular momentum LL, with its nodal structure in List-II. List-IList-IIP)n=4, L=6 h2π1)1 radial node, 2 angular nodesQ)n=5, L=2 h2π2)3 radial nodes, 1 angular nodeR)n=3, L=03)2 radial nodes, no angular nodeS)n=6, L=12 h2π4)2 radial nodes, 3 angular nodes5)no radial node, 3 angular nodes\begin{array}{ll} \textbf{List-I} & \textbf{List-II} \\ \text{P)} n=4,\ L=\sqrt{6}\,\dfrac{h}{2\pi} & \text{1)} \text{1 radial node, 2 angular nodes} \\ \text{Q)} n=5,\ L=\sqrt{2}\,\dfrac{h}{2\pi} & \text{2)} \text{3 radial nodes, 1 angular node} \\ \text{R)} n=3,\ L=0 & \text{3)} \text{2 radial nodes, no angular node} \\ \text{S)} n=6,\ L=\sqrt{12}\,\dfrac{h}{2\pi} & \text{4)} \text{2 radial nodes, 3 angular nodes} \\ & \text{5)} \text{no radial node, 3 angular nodes} \end{array}
Not attempted
A
P-1, Q-2, R-4, S-3
B
P-2, Q-1, R-3, S-5
C
P-5, Q-2, R-1, S-4
D
P-1, Q-2, R-3, S-4
57
In a hypothetical universe the quantum numbers nn, ll and mlm_l obey the usual rules, but the spin quantum number can take THREE values (ms=−1,0,+1m_s=-1,0,+1) and the Pauli exclusion principle still forbids two electrons from having all quantum numbers the same. Subshells fill in the usual order of increasing (n+l)(n+l), with lower nn first when (n+l)(n+l) is equal. What is the atomic number of the element whose ground state has the 3p3p subshell just completely filled?
Not attempted
Your answer: —
Correct answer: 27
58
For a filled subshell, or for a subshell in which each orbital holds one electron and all electron spins are parallel, the total electron density summed over the electrons of the subshell is spherically symmetric. In its ground state, which of the following free ions has a spherically symmetric electron cloud overall (every subshell of the ion is of one of these two kinds)?
Not attempted
A
Fe2+\text{Fe}^{2+}
B
Mn2+\text{Mn}^{2+}
C
Cr3+\text{Cr}^{3+}
D
Co2+\text{Co}^{2+}
59
Which of the following statements about the hydrogen atom orbitals is/are correct? (a0a_0 is the Bohr radius.)
Not attempted
A
The radial probability distribution 4πr2ψ24\pi r^{2}\psi^{2} of the 3s3s orbital has three maxima, separated by two radial nodes.
B
The probability density ψ2\psi^{2} of a 2s2s electron is zero at the nucleus because the 2s2s orbital has a radial node.
C
The 3p3p orbital has one radial node and one angular node, and its radial probability distribution has two maxima.
D
The highest maximum of the radial distribution of the 2s2s orbital lies at 4a04a_0, the same distance as the single maximum of the 2p2p orbital.
60
The electron of a hydrogen atom has principal quantum number n=4n=4, and its orbital has exactly one nodal plane through the nucleus. Each graph below shows 4πr2ψ24\pi r^{2}\psi^{2} against rr on the same scale of distance (in units of the Bohr radius a0a_0; each graph is scaled to its own highest peak). Which graph shows the radial probability distribution of this electron?
Not attempted
A
Graph 2
r (a₀)4πr²ψ²O10203040
B
Graph 3
r (a₀)4πr²ψ²O10203040
C
Graph 1
r (a₀)4πr²ψ²O10203040
D
Graph 4
r (a₀)4πr²ψ²O10203040
61
Find the total number of unpaired electrons in the ground states of the following seven species taken together: Cr\text{Cr}, Cu\text{Cu}, Fe3+\text{Fe}^{3+}, Co2+\text{Co}^{2+}, Ni\text{Ni}, Zn\text{Zn} and V3+\text{V}^{3+}. (Use the usual exceptions for Cr\text{Cr} and Cu\text{Cu}, and remove the outermost-shell electrons first when forming cations.)
Not attempted
Your answer: —
Correct answer: 19
62
Which of the following statements is/are correct for ground-state electronic configurations? (Use the usual exceptions for Cr\text{Cr} and Cu\text{Cu}.)
Not attempted
A
The copper atom has 77 electrons with l=0l=0, 1212 electrons with l=1l=1 and 1010 electrons with l=2l=2.
B
The chromium atom has 88 electrons with l=0l=0.
C
Fe3+\text{Fe}^{3+} and Mn2+\text{Mn}^{2+} have the same electronic configuration, [Ar] 3d5[\text{Ar}]\,3d^{5}, and therefore the same number of unpaired electrons.
D
Cr3+\text{Cr}^{3+} has the configuration [Ar] 3d24s1[\text{Ar}]\,3d^{2}4s^{1}.
63
Which orbital-box diagram shows the ground state of a free chromium atom (only the 3d3d and 4s4s levels are drawn; arrows show the spin of each electron)?
Not attempted
A
Diagram 1
3d4s
B
Diagram 2
3d4s
C
Diagram 3
3d4s
D
Diagram 4
3d4s
64
Suppose the (n+l)(n+l) rule (subshells fill in order of increasing n+ln+l, and for equal n+ln+l the lower nn first) held without exception for all elements, however heavy. What would be the atomic number of the first element whose ground state contains an electron with l=4l=4 (a gg electron)?
Not attempted
Your answer: —
Correct answer: 121
65
Six neutral atoms are described by the outer part of their configuration, written after the argon core [Ar][\text{Ar}]: atom with Z=24Z=24: 3d44s23d^{4}4s^{2}; atom with Z=29Z=29: 3d104s13d^{10}4s^{1}; atom with Z=30Z=30: 3d104s23d^{10}4s^{2}; atom with Z=28Z=28: 3d94s13d^{9}4s^{1}; atom with Z=25Z=25: 3d54s23d^{5}4s^{2}; atom with Z=23Z=23: 3d44s13d^{4}4s^{1}. For how many of these atoms is the configuration given the correct ground-state configuration? (Use the standard ground-state configurations, with Cr\text{Cr} and Cu\text{Cu} as the only exceptions to the simple filling order.)
Not attempted
Your answer: —
Correct answer: 3
66
The spin-only magnetic moment is μ=n(n+2)\mu=\sqrt{n(n+2)} BM, where nn is the number of unpaired electrons. For the ground-state free ions (remove 4s4s electrons first), which of the following statements is/are correct?
Not attempted
A
Cr2+\text{Cr}^{2+} and Fe3+\text{Fe}^{3+} have the same spin-only magnetic moment.
B
Ti3+\text{Ti}^{3+} and Cu2+\text{Cu}^{2+} have the same spin-only magnetic moment, 1.731.73 BM, although their dd subshells are far from alike.
C
Ni2+\text{Ni}^{2+} and V3+\text{V}^{3+} have the same spin-only magnetic moment, 2.832.83 BM.
D
Co2+\text{Co}^{2+} has a spin-only magnetic moment of 5.925.92 BM.
67
Among the elements with atomic numbers 11 to 3636, how many have exactly two unpaired electrons in the ground state of the neutral atom? (Use the usual exceptions for Cr\text{Cr} and Cu\text{Cu}.)
Not attempted
Your answer: —
Correct answer: 8
68
Match each species in List-I with its spin-only magnetic moment in List-II (use μ=n(n+2)\mu=\sqrt{n(n+2)} BM, nn = number of unpaired electrons). List-IList-IIP)Ground-state Cr atom1)1.73 BMQ)Ground-state Cu atom2)3.87 BMR)Fe2+3)4.90 BMS)Co2+4)5.92 BM5)6.93 BM\begin{array}{ll} \textbf{List-I} & \textbf{List-II} \\ \text{P)} \text{Ground-state }\text{Cr}\text{ atom} & \text{1)} \text{1.73 BM} \\ \text{Q)} \text{Ground-state }\text{Cu}\text{ atom} & \text{2)} \text{3.87 BM} \\ \text{R)} \text{Fe}^{2+} & \text{3)} \text{4.90 BM} \\ \text{S)} \text{Co}^{2+} & \text{4)} \text{5.92 BM} \\ & \text{5)} \text{6.93 BM} \end{array}
Not attempted
A
P-5, Q-1, R-3, S-2
B
P-4, Q-2, R-3, S-1
C
P-5, Q-3, R-1, S-2
D
P-3, Q-1, R-5, S-4
69
In a many-electron atom the order of energy of subshells follows the (n+l)(n+l) rule, with the lower nn lower in energy when (n+l)(n+l) is equal. Which is the correct order of increasing energy of the subshells 5p5p, 4f4f, 6s6s, 4d4d and 5d5d?
Not attempted
A
6s<5p<4d<4f<5d6s<5p<4d<4f<5d
B
4d<5p<6s<5d<4f4d<5p<6s<5d<4f
C
4d<5p<6s<4f<5d4d<5p<6s<4f<5d
D
4f<4d<5p<5d<6s4f<4d<5p<5d<6s
70
The figure shows seven orbital-box diagrams for the three 2p2p orbitals (arrows show electron spins). Each is meant to represent the ground-state arrangement of the 2p2p electrons of some neutral atom from boron to neon. How many of the seven diagrams are possible ground-state arrangements, i.e. obey both the Pauli exclusion principle and Hund's rule of maximum multiplicity?
Not attempted
(1)(2)(3)(4)(5)(6)(7)
Your answer: —
Correct answer: 4
Check each diagram for (i) no orbital with two parallel spins, and (ii) the maximum number of unpaired electrons with parallel spins that the electron count allows.
Diagram (1): one electron, fine. (2): two electrons paired in one orbital while two orbitals are empty. Hund's rule requires them in different orbitals with parallel spins: not ground state. (3): three electrons, one in each orbital, all parallel: nitrogen, correct. (4): three electrons with a pair although an orbital is empty: violates Hund's rule. (5): ↑↓,↑,↑\uparrow\downarrow,\uparrow,\uparrow: four electrons, one pair and two parallel singles: oxygen, correct. (6): ↑↓,↑↓,↑\uparrow\downarrow,\uparrow\downarrow,\uparrow: five electrons, fluorine, correct. (7): ↑,↓,↑\uparrow,\downarrow,\uparrow: three electrons in three orbitals but one spin is antiparallel; maximum multiplicity requires all three parallel, so this is an excited arrangement. Valid: (1), (3), (5), (6): 44.