Q.No:1 JEST-2012
Consider the Bohr model of the hydrogen atom. If \(\alpha\) is the fine-structure constant, the velocity of the electron in its lowest orbit is
(a)
\(\frac{c}{1+\alpha}\)
(b)
\(\frac{c}{1+\alpha^2}\) or \((1-\alpha)c\)
(c)
\(\alpha^2 c\)
(d)
\(\alpha c\)
Check Answer
Option d
Q.No:2 JEST-2012
The binding energy of the hydrogen atom (electron bound to proton) is \(13.6 eV\). The binding energy of positronium (electron bound to positron) is
(a)
\(13.6/2 eV\)
(b)
\(13.6/1810 eV\)
(c)
\(13.6\times 1810 eV\)
(d)
\(13.6\times 2 eV\)
Check Answer
Option a
Q.No:3 JEST-2012
A sodium atom in the first excited \(3P\) state has a lifetime of \(16 ns\) for decaying to the ground \(3S\) state. The wavelength of the emitted photon is \(589 nm\). The corresponding linewidth of the transition (in frequency units) is about
(a)
\(1.7\times 10^6 Hz\)
(b)
\(1\times 10^7 Hz\)
(c)
\(6.3\times 10^7 Hz\)
(d)
\(5\times 10^{14} Hz\)
Check Answer
Option b
Q.No:4 JEST-2013
If a proton were ten times lighter, the ground state energy of the electron in a hydrogen atom would be
(a)
less
(b)
more
(c)
the same
(d)
less, more or equal depending on the electron mass
Check Answer
Option a
Q.No:5 JEST-2013
The binding energy of the \(k\)-shell electron in a Uranium atom (\(Z=92; A=238\)) will be modified due to (i) screening caused by other electrons and (ii) the finite extent of the nucleus as follows:
(a)
increases due to (i), remains unchanged due to (ii).
(b)
decreases due to (i), decreases due to (ii).
(c)
increases due to (i), increases due to (ii).
(d)
decreases due to (i), remains unchanged due to (ii).
Check Answer
Option b
Q.No:6 JEST-2014
A hydrogen atom in its ground state is collided with an electron of kinetic energy \(13.377 eV\). The maximum factor by which the radius of the atom would increase is
(a)
\(7\)
(b)
\(8\)
(c)
\(49\)
(d)
\(64\)
Check Answer
Option c
Q.No:7 JEST-2014
Which functional form of potential best describes the interaction between a neutral atom and an ion at large distances (i.e. much larger than their diameters)
(a)
\(V\propto -1/r^2\)
(b)
\(V\propto -1/r\)
(c)
\(V\propto -e^{-r/a}/r\)
(d)
\(V\propto -1/r^3\)
Check Answer
Option a
Q.No:8 JEST-2014
If a proton were ten times lighter, then the ground state energy of the electron in a hydrogen atom would have been
(a)
Less
(b)
The same
(c)
More
(d)
Depends on the electron mass
Check Answer
Option b
Q.No:9 JEST-2014
If hydrogen atom is bombarded by energetic electrons, it will emit
(a)
\(K_{\alpha}\) X-rays
(b)
\(\beta\)-rays
(c)
neutrons
(d)
none of the above
Check Answer
Option d
Q.No:10 JEST-2015
The energy difference between the \(3p\) and \(3s\) levels in \({Na}\) is \(2.1 eV\). Spin-orbit coupling splits the \(3p\) level, resulting in two emission lines differing by \(6\) Angstrom. The splitting of the \(3p\) level is approximately,
(a)
\(2 eV\)
(b)
\(0.2 eV\)
(c)
\(0.02 eV\)
(d)
\(2 meV\)
Check Answer
Option d
Q.No:11 JEST-2015
Which of the following statements is true for the energies of the terms of the carbon atom in the ground state electronic configuration \(1s^2 2s^2 2p^2\)?
(a)
\({}^3 P<^1 D <^1 S\)
(b)
\({}^3 P<^1 S <^1 D\)
(c)
\({}^3 P<^1 F <^1 S\)
(d)
\({}^3 P<^1 F <^1 D\)
Check Answer
Option a
Q.No:12 JEST-2016
If the Rydberg constant of an atom of finite nuclear mass is \(\alpha R_{\infty}\), where \(R_{\infty}\) is the Rydberg constant corresponding to an infinite nuclear mass, the ratio of the electronic to nuclear mass of the atom is:
(A)
\((1-\alpha)/\alpha\)
(B)
\((\alpha-1)/\alpha\)
(C)
\((1-\alpha)\)
(D)
\(1/\alpha\)
Check Answer
Option A
Q.No:13 JEST-2019
What is the binding energy of an electron in the ground state of a \({He^{+}}\) ion?
(A)
\(6.8 eV\)
(B)
\(13.6 eV\)
(C)
\(27.2 eV\)
(D)
\(54.4 eV\)
Check Answer
Option D
Q.No:14 JEST-2019
Consider a hypothetical world in which the electron has spin \(\frac{3}{2}\) instead of \(\frac{1}{2}\). What will be the electronic configuration for an element with atomic number \(Z=5\)?
(A)
\(1s^4, 2s^1\)
(B)
\(1s^2, 2s^2, 2p^1\)
(C)
\(1s^5\)
(D)
\(1s^3, 2s^1, 2p^1\)
Check Answer
Option A
Q.No:15 JEST-2021
Positronium is a short lived bound state of an electron and a positron. The energy difference between the first excited state and ground state of positronium is expected to be around
(A)
four times that of the Hydrogen atom
(B)
twice that of the Hydrogen atom
(C)
half that of the Hydrogen atom
(D)
the same as that of the Hydrogen atom
Check Answer
Option C
Q.No:16 JEST-2025
Given the mass of the proton \(m_p \simeq 1836\,m_e\) and the mass of the deuteron
\(m_d \simeq 3670\,m_e\), where \(m_e\) is the electron mass, find the fractional
shift (in parts per million, to the nearest integer) of the ground state energy
of the deuterium atom as compared to the hydrogen atom.
Check Answer
ANS 272
Q.No:1 TIFR-2012
Consider the high excited states of a Hydrogen atom corresponding to large values of the principal quantum number (\(n\gg 1\)). The wavelength \(\lambda\) of a photon emitted due to an electron undergoing a transition between two such states with consecutive values of \(n\) (i.e. \(\psi_{n+1}\to \psi_n\)) is related to the wavelength \(\lambda_{\alpha}\) of the \(K_{\alpha}\) line of Hydrogen by
(a)
\(\lambda=n^3 \lambda_{\alpha}/8\)
(b)
\(\lambda=3n^3 \lambda_{\alpha}/8\)
(c)
\(\lambda=n^2 \lambda_{\alpha}\)
(d)
\(\lambda=4\lambda_{\alpha}/n^2\)
Check Answer
Option b
Q.No: 2 TIFR-2012
When light is emitted from a gas of excited atoms, the lines in the spectrum are Doppler-broadened due to the thermal motion of the emitting atoms.
The Doppler width of an emission line of wavelength \(500\) nanometres (nm) emitted by an excited atom of Argon \(({^{40}_{20} A})\) at room temperature (\(27^{\circ}C\)) can be estimated as
(a)
\(5.8\times 10^{-4} nm\)
(b)
\(3.2\times 10^{-4} nm\)
(c)
\(3.2\times 10^{-3} nm\)
(d)
\(2.5\times 10^{-3} nm\)
(e)
\(1.4\times 10^{-3} nm\)
Check Answer
Option e
Q.No: 3 TIFR-2013
The velocity of an electron in the ground state of a hydrogen atom is \(v_H\). If \(v_p\) be the velocity of an electron in the ground state of positronium, then
(a)
\(v_p=v_H\)
(b)
\(v_p=2v_H\)
(c)
\(v_p=v_H/2\)
(d)
\(v_p=\sqrt{2}v_H\)
Check Answer
Option a
Q.No: 4 TIFR-2013
When a pure element is vaporised and placed in a uniform magnetic field \(B_0\), it is seen that a particular spectral line of wavelength \(\lambda\), corresponding to a \(J=1\to J=0\) transition, gets split into three components \(\lambda, \lambda\pm \Delta \lambda\). It follows that the Land{\' e} \(g\)-factor for the transition \(J=1\to J=0\) is given by
(a)
\(g=\frac{hc}{\mu_B B_0}\frac{\Delta \lambda^2}{\lambda}\)
(b)
\(g=\frac{hc}{\mu_B B_0}\frac{\lambda}{\Delta \lambda^2}\)
(c)
\(g=\frac{hc}{\mu_B B_0}\frac{\lambda^2}{\Delta \lambda}\)
(d)
\(g=\frac{hc}{\mu_B B_0}\frac{\Delta \lambda}{\lambda^2}\)
Check Answer
Option d
Q.No: 5 TIFR-2014
The ground state electronic configuration for a carbon atom is
\[
(1s)^2 (2s)^2 (2p)^2.
\]
The first excited state of this atom would be achieved by
(a)
re-alignment of the electron spins within the \(2p\) orbital.
(b)
transition of an electron from the \(2s\) orbital to the \(2p\) orbital.
(c)
transition of an electron from the \(2p\) orbital to the \(3s\) orbital.
(d)
transition of an electron from the \(2s\) orbital to the \(3s\) orbital.
Check Answer
Option a
Q.No: 6 TIFR-2015
A sample of ordinary hydrogen \(({^{1}_{1} H})\) gas in a discharge tube was seen to emit the usual Balmer spectrum. On careful examination, however, it was found that the \(H_{\alpha}\) line in the spectrum was split into two fine lines, one an intense line at \(656.28 nm\), and the other a faint line at \(656.04 nm\). From this, one can conclude that the gas sample had a small impurity of
(a)
\({^{2}_{1} H}\)
(b)
\({^{3}_{1} H}\)
(c)
\({^{4}_{2} He}\)
(d)
\({H_{2} O}\)
Check Answer
Option b
Q.No: 7 TIFR-2015
In the ground state electronic configuration of nitrogen \(({^{14}_{7} N})\) the \(L, S\) and \(J\) quantum numbers are
(a)
\(L=1, S=1/2, J=1/2\)
(b)
\(L=1, S=1/2, J=3/2\)
(c)
\(L=0, S=1/2, J=1/2\)
(d)
\(L=0, S=3/2, J=3/2\)
Check Answer
Option d
Q.No: 8 TIFR-2017
The energy of an electron in the ground state of the \({He}\) atom is \(-79 \hspace{1mm}\text{eV}\). Considering the Bohr model of the atom, what would be \(10\) times the first ionization potential for a \({He^{+}}\) ion, in units of \(\text{eV}\)?
Check Answer
Ans 246
Q.No: 9 TIFR-2018
The electron of a free hydrogen atom is initially in a state with quantum numbers \(n=3\) and \(\ell=2\). It then makes an electric dipole transition to a lower energy state. Which one of the given states could it be in after the transition?
(a)
\(n=2, \ell=1\)
(b)
\(n=2, \ell=2\)
(c)
\(n=3, \ell=0\)
(d)
\(n=3, \ell=1\)
Check Answer
Option a
Q.No: 10 TIFR-2020
A sample of hydrogen gas was placed in a discharge tube and its spectrum was measured using a high-resolution spectrometer. The \(H_{\alpha}\) line in the spectrum was found to be split into two lines, a high intensity line at \(656.28 \hspace{1mm}\text{nm}\), and a low intensity line at \(656.01\hspace{1mm}\text{nm}\). This indicates that the hydrogen sample was contaminated with
(a)
deuterium
(b)
tritium
(c)
helium
(d)
water vapour
Check Answer
Option c
Q.No: 11 TIFR-2021
A hydrogen atom in its ground state collides with an electron of energy \(13.377 \hspace{1mm}\text{eV}\), absorbs most of the energy of the electron, and goes into an excited state. The maximum possible fraction
\[
f\equiv \frac{R_{\text{final}}-R_{\text{initial}}}{R_{\text{initial}}}
\]
by which its radius \(R\) would increase will be
(a)
\(f=0.63\)
(b)
\(f=0.48\)
(c)
\(f=0.60\)
(d)
\(f=0.07\)
Check Answer
Option a
Q.No: 12 TIFR-2022
A gas of atoms, each of mass \(m\), in thermal equilibrium at a temperature \(T\), is radiating with a frequency \(v_0\). The Doppler broadening (full width at half maximum, or FWHM) of the observed spectral line would be given by
(a)
\(\frac{2 v_0}{c} \sqrt{\frac{2 \hspace{0.5mm} ln \hspace{0.5mm} 2 \hspace{0.5mm} k_B T}{m}}\)
(b)
\(\frac{ v_0}{c} \sqrt{\frac{2 k_B T}{m}}\)
(c)
\(\frac{2 v_0}{c} \sqrt{\frac{ ln \hspace{0.5mm} 2 \hspace{0.5mm} k_B T}{m}}\)
(d)
\(\frac{2 v_0}{c} \sqrt{\frac{2 k_B T}{m}}\)
Check Answer
Option a
Q.No: 13 TIFR-2022
In a semiclassical approach, the Hamiltonian of a He atom is modified by adding a magnetic interaction term between the two electrons, of the form
\[H_1=A_2 \hspace{0.3mm} \vec{S_1} \cdot \vec{S_2} \]
where \(\vec{S_1}\) and \(\vec{S_2}\) are the electron spins and \(A_2\) is a coupling constant. This leads, for the configuration \(1s^2\), to the energy shift
(a)
\(-3A_2/4\)
(b)
\(+3A_2/4\)
(c)
\(+A_2/4\)
(d)
\(-A_2/4\)
Check Answer
Option a
Q.No: 14 TIFR-2023
An atom of mass \(M\) at rest emits or absorbs a photon of frequency \(v\) and recoils with a momentum \(p\). The frequency of the internal transition of electronic levels is \(v_0\) without accounting for recoil. Assuming the process is nonrealistic, the fractional differences between the photon frequency for emission and absorption \((v-v_0)/v\), respectively, are given by
(a)
\(+\frac{h v_0}{2M c^2}\) (emission), \(-\frac{h v_0}{2M c^2}\) (absorption)
(b)
\(+\frac{h v}{M c^2}\) (emission), \(-\frac{h v}{M c^2}\) (absorption)
(c)
\(-\frac{h v}{2M c^2}\) (emission), \(+\frac{h v}{2M c^2}\) (absorption)
(d)
\(-\frac{h v_0}{M c^2}\) (emission), \(+\frac{h v_0}{M c^2}\) (absorption)
Check Answer
Option c
Q.No: 15 TIFR-2023
The number of hyperfine states found in the \(^3 He\) atom for the electronic configuration
\[1s^1 2s^0 2p^1\]
would be
(c)
7
(c)
2
(c)
4
(c)
1
Check Answer
Option a
Q.No: 16 TIFR-2024
The ionization potential of the H atom is 13.598 eV. If the mass of a proton is \( 1.673 \times 10^{-27} \) kg, the mass of an electron is \( 9.109 \times 10^{-31} \) kg and the mass of the D nucleus is \( 3.344 \times 10^{-27} \) kg, the ionization potential of the D atom is given by:
(a) \( 13.602 \) eV
(b) \( 13.594 \) eV
(c) \( 13.598 \) eV
(d) \( 27.188 \) eV
Check Answer
Option a
Q.No: 17 TIFR-2025
In the shell model of a nucleus, states of nucleons (protons or neutrons) in a
spherically symmetric potential are labelled as \(nL_j\), where \(n\) is the
principal quantum number, \(L\) is the orbital angular momentum quantum number
(\(s,p,d,f\) correspond to \(L=0,1,2,3\) respectively), and
\(\vec{J} = \vec{L} + \vec{S}\).
The spin–orbit interaction is given by
\[
\hat{H}_{so} = C\, \vec{L}\cdot\vec{S}.
\]
If the strength of the spin–orbit interaction is \(C = -2\,\text{MeV}\), the
energy difference between the two nucleonic states
\(1d_{5/2}\) and \(1d_{3/2}\) is
a) 5 MeV
b) 2 MeV
c) 3 MeV
d) 4 MeV
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