Atoms and Nuclei
299 Questions
Start JEE Mains Test
2021
Q201
JEE Mains
Numerical
10 Mar 2026
The first three spectral lines of H-atom in the Balmer series are
given $\lambda$1, $\lambda$2, $\lambda$3 considering the Bohr atomic model, the wave lengths of first and third spectral lines $\left( \frac{\lambda_{1} }{\lambda_{3} } \right) $ are related by a factor of approximately 'x' $\times$ 10$-$1.
The value of x, to the nearest integer, is _________.
given $\lambda$1, $\lambda$2, $\lambda$3 considering the Bohr atomic model, the wave lengths of first and third spectral lines $\left( \frac{\lambda_{1} }{\lambda_{3} } \right) $ are related by a factor of approximately 'x' $\times$ 10$-$1.
The value of x, to the nearest integer, is _________.
Correct Answer: 15
Explanation:
For 1st line
${1 \over {{\lambda _1}}} = R{z^2}\left( {{1 \over {{2^2}}} - {1 \over {{3^2}}}} \right)$
${1 \over {{\lambda _1}}} = R{z^2}{5 \over {36}}$ ..... (i)
For 3rd line
${1 \over {{\lambda _3}}} = R{z^2}\left( {{1 \over {{2^2}}} - {1 \over {{5^2}}}} \right)$
${1 \over {{\lambda _3}}} = R{z^2}{{21} \over {100}}$ ...... (ii)
Dividing (ii) by (i),
${{{\lambda _1}} \over {{\lambda _3}}} = {{21} \over {100}} \times {{36} \over 5} = 1.512 = 15.12 \times {10^{ - 1}}$
$x \approx 15$
${1 \over {{\lambda _1}}} = R{z^2}\left( {{1 \over {{2^2}}} - {1 \over {{3^2}}}} \right)$
${1 \over {{\lambda _1}}} = R{z^2}{5 \over {36}}$ ..... (i)
For 3rd line
${1 \over {{\lambda _3}}} = R{z^2}\left( {{1 \over {{2^2}}} - {1 \over {{5^2}}}} \right)$
${1 \over {{\lambda _3}}} = R{z^2}{{21} \over {100}}$ ...... (ii)
Dividing (ii) by (i),
${{{\lambda _1}} \over {{\lambda _3}}} = {{21} \over {100}} \times {{36} \over 5} = 1.512 = 15.12 \times {10^{ - 1}}$
$x \approx 15$
2020
Q202
JEE Mains
MCQ
10 Mar 2026
Given the masses of various atomic particles
mp = 1.0072 u, mn = 1.0087 u, me = 0.000548 u,
${m_{\overline v }}$ = 0, md = 2.0141 u, where p $ \equiv $ proton, n $ \equiv $ neutron,
e $ \equiv $ electron, $\overline v $ $ \equiv $ antineutrino and d $ \equiv $ deuteron. Which of the following process is allowed by momentum and energy conservation?
mp = 1.0072 u, mn = 1.0087 u, me = 0.000548 u,
${m_{\overline v }}$ = 0, md = 2.0141 u, where p $ \equiv $ proton, n $ \equiv $ neutron,
e $ \equiv $ electron, $\overline v $ $ \equiv $ antineutrino and d $ \equiv $ deuteron. Which of the following process is allowed by momentum and energy conservation?
A.
n + n $ \to $ deuterium atom
(electron bound to the nucleus)
(electron bound to the nucleus)
B.
n + p $ \to $ d + $\gamma $
C.
p $ \to $ n + e+ + $\overline v $
D.
e+ + e- $ \to $ $\gamma $
2020
Q203
JEE Mains
MCQ
10 Mar 2026
You are given that Mass of ${}_3^7Li$ = 7.0160u,
Mass of ${}_2^4He$ = 4.0026u
and Mass of ${}_1^1H$ = 1.0079u.
When 20 g of ${}_3^7Li$ is converted into ${}_2^4He$ by proton capture, the energy liberated, (in kWh), is :
[Mass of nucleon = 1 GeV/c2]
Mass of ${}_2^4He$ = 4.0026u
and Mass of ${}_1^1H$ = 1.0079u.
When 20 g of ${}_3^7Li$ is converted into ${}_2^4He$ by proton capture, the energy liberated, (in kWh), is :
[Mass of nucleon = 1 GeV/c2]
A.
6.82 $ \times $ 105
B.
4.5 $ \times $ 105
C.
8 $ \times $ 106
D.
1.33 $ \times $ 106
2020
Q204
JEE Mains
MCQ
10 Mar 2026
A radioactive nucleus decays by two different
processes. The half life for the first process is
10 s and that for the second is 100 s. The
effective half life of the nucleus is close to :
A.
12 sec
B.
9 sec
C.
55 sec
D.
6 sec
2020
Q205
JEE Mains
MCQ
10 Mar 2026
Activities of three radioactive substances A, B
and C are represented by the curves A, B and
C, in the figure. Then their half-lives
${T_{{1 \over 2}}}\left( A \right)$ : ${T_{{1 \over 2}}}\left( B \right)$ : ${T_{{1 \over 2}}}\left( C \right)$ are in the ratio :
${T_{{1 \over 2}}}\left( A \right)$ : ${T_{{1 \over 2}}}\left( B \right)$ : ${T_{{1 \over 2}}}\left( C \right)$ are in the ratio :
A.
3 : 2 : 1
B.
2 : 1 : 1
C.
4 : 3 : 1
D.
2 : 1 : 3
2020
Q206
JEE Mains
MCQ
10 Mar 2026
Find the Binding energy per neucleon for ${}_{50}^{120}Sn$. Mass of proton mp
= 1.00783 U, mass of neutron
mn
= 1.00867 U and mass of tin nucleus mSn = 119.902199 U. (take 1U = 931 MeV)
A.
9.0 MeV
B.
8.5 MeV
C.
8.0 MeV
D.
7.5 MeV
2020
Q207
JEE Mains
MCQ
10 Mar 2026
Hydrogen ion and singly ionized helium atom are accelerated, from rest, through the same potential
difference. The ratio of final speeds of hydrogen and helium ions is close to :
A.
2 : 1
B.
1 : 2
C.
5 : 7
D.
10 : 7
2020
Q208
JEE Mains
MCQ
10 Mar 2026
The radius R of a nucleus of mass number A can be estimated by the formula
R = (1.3 $ \times $ 10–15)A1/3 m.
It follows that the mass density of a nucleus is of the order of :
(Mprot. $ \cong $ Mneut $ \simeq $ 1.67 $ \times $ 10–27 kg)
R = (1.3 $ \times $ 10–15)A1/3 m.
It follows that the mass density of a nucleus is of the order of :
(Mprot. $ \cong $ Mneut $ \simeq $ 1.67 $ \times $ 10–27 kg)
A.
1024 kg m–3
B.
1010 kg m–3
C.
1017 kg m–3
D.
103 kg m–3
2020
Q209
JEE Mains
MCQ
10 Mar 2026
In a radioactive material, fraction of active
material remaining after time t is 9/16. The
fraction that was remaining after t/2 is
A.
${3 \over 4}$
B.
${4 \over 5}$
C.
${3 \over 5}$
D.
${7 \over 8}$
2020
Q210
JEE Mains
MCQ
10 Mar 2026
In a hydrogen atom the electron makes a
transition from (n + 1)th level to the nth level.
If n >> 1, the frequency of radiation emitted is
proportional to :
A.
${1 \over n}$
B.
${1 \over {{n^2}}}$
C.
${1 \over {{n^3}}}$
D.
${1 \over {{n^4}}}$
2020
Q211
JEE Mains
MCQ
10 Mar 2026
In a reactor, 2 kg of 92U235 fuel is fully used up
in 30 days. The energy released per fission is
200 MeV. Given that the Avogadro number,
N = 6.023 $ \times $ 1026 per kilo mole and 1 eV =
1.6 × 10–19 J. The power output of the reactor is
close to
A.
125 MW
B.
60 MW
C.
54 MW
D.
35 MW
2020
Q212
JEE Mains
MCQ
10 Mar 2026
The energy required to ionise a hydrogen like
ion in its ground state is 9 Rydbergs. What is
the wavelength of the radiation emitted when
the electron in this ion jumps from the second
excited state to the ground state ?
A.
35.8 nm
B.
11.4 nm
C.
8.6 nm
D.
24.2 nm
2020
Q213
JEE Mains
MCQ
10 Mar 2026
The graph which depicts the results of
Rutherford gold foil experiment with
$\alpha $-particales is :
$\theta $ : Scattering angle
Y : Number of scattered $\alpha $-particles detected (Plots are schematic and not to scale)
$\theta $ : Scattering angle
Y : Number of scattered $\alpha $-particles detected (Plots are schematic and not to scale)
A.
B.
C.
D.
2020
Q214
JEE Mains
MCQ
10 Mar 2026
The activity of a radioactive sample falls from 700 s–1 to 500 s–1 in 30 minutes. Its half life is close
to:
A.
62 min
B.
66 min
C.
72 min
D.
52 min
2020
Q215
JEE Mains
MCQ
10 Mar 2026
The time period of revolution of electron in its ground state orbit in a hydrogen atom is 1.6 $ \times $ 10-16 s. The frequency of revolution of the electron in its first excited state (in s-1) is :
A.
5.6 $ \times $ 1012
B.
1.6 $ \times $ 1014
C.
7.8 $ \times $ 1014
D.
6.2 $ \times $ 1015
2020
Q216
JEE Mains
Numerical
10 Mar 2026
A particle of mass 200 MeV/c2 collides with a
hydrogen atom at rest. Soon after the collision
the particle comes to rest, and the atom
recoils and goes to its first excited state. The
initial kinetic energy of the particle (in eV) is
${N \over 4}$. The value of N is :
(Given the mass of the hydrogen atom to be 1 GeV/c2) ______ .
${N \over 4}$. The value of N is :
(Given the mass of the hydrogen atom to be 1 GeV/c2) ______ .
Correct Answer: 51
Explanation:
Given, mparticle = 200 MeV/c2 = m(Assume)
and mH = 1 GeV/c2 = 1000 MeV/c2 = 5 $ \times $ 200 = 5m
Applying momentum conservation,
pi = pf
$ \Rightarrow $ mv0 + 0 = 0 + 5 mv'
$ \Rightarrow $ v' = ${{{v_0}} \over 5}$
Initial kinetic energy, ki = ${1 \over 2}mv_0^2$
Final kinetic energy, kf = ${1 \over 2}\left( {5m} \right){\left( {{{{v_0}} \over 5}} \right)^2}$
$ \therefore $ Loss in KE
= ${1 \over 2}mv_0^2$ - ${1 \over 2}\left( {5m} \right){\left( {{{{v_0}} \over 5}} \right)^2}$
= ${4 \over 5}\left( {{1 \over 2}mv_0^2} \right)$ = ${4 \over 5}\left( {{k_i}} \right)$
This lost energy is used by the hydrogen atom to move from ground state to the first excited state. We know the the energy required by the hydrogen atom to move from ground state to first excited state is 10.2 eV.
$ \therefore $ ${4 \over 5}\left( {{k_i}} \right)$ = 10.2
$ \Rightarrow $ ki = ${{5 \times 10.2} \over 4} = {{51} \over 4}$
$ \therefore $ N = 51
and mH = 1 GeV/c2 = 1000 MeV/c2 = 5 $ \times $ 200 = 5m
Applying momentum conservation,
pi = pf
$ \Rightarrow $ mv0 + 0 = 0 + 5 mv'
$ \Rightarrow $ v' = ${{{v_0}} \over 5}$
Initial kinetic energy, ki = ${1 \over 2}mv_0^2$
Final kinetic energy, kf = ${1 \over 2}\left( {5m} \right){\left( {{{{v_0}} \over 5}} \right)^2}$
$ \therefore $ Loss in KE
= ${1 \over 2}mv_0^2$ - ${1 \over 2}\left( {5m} \right){\left( {{{{v_0}} \over 5}} \right)^2}$
= ${4 \over 5}\left( {{1 \over 2}mv_0^2} \right)$ = ${4 \over 5}\left( {{k_i}} \right)$
This lost energy is used by the hydrogen atom to move from ground state to the first excited state. We know the the energy required by the hydrogen atom to move from ground state to first excited state is 10.2 eV.
$ \therefore $ ${4 \over 5}\left( {{k_i}} \right)$ = 10.2
$ \Rightarrow $ ki = ${{5 \times 10.2} \over 4} = {{51} \over 4}$
$ \therefore $ N = 51
2020
Q217
JEE Mains
Numerical
10 Mar 2026
The first member of the Balmer series of
hydrogen atom has a wavelength of 6561 Å.
The wavelength of the second member of the
Balmer series (in nm) is:
Correct Answer: 486
Explanation:
${1 \over {{\lambda _1}}} = R{Z^2}\left( {{1 \over {{2^2}}} - {1 \over {{3^2}}}} \right)$ = ${5 \over {36}}$RZ2
${1 \over {{\lambda _2}}} = R{Z^2}\left( {{1 \over {{2^2}}} - {1 \over {{4^2}}}} \right)$ = ${{12} \over {64}}$RZ2
$ \therefore $ ${{{\lambda _2}} \over {{\lambda _1}}}$ = ${5 \over {36}} \times {{64} \over {12}}$ = ${{20} \over {27}}$
$ \Rightarrow $ $\lambda $2 = ${{20} \over {27}}{\lambda _1}$
= ${{20} \over {27}}$ $ \times $ 6561 = 4860 $\mathop A\limits^o $ = 486 nm
${1 \over {{\lambda _2}}} = R{Z^2}\left( {{1 \over {{2^2}}} - {1 \over {{4^2}}}} \right)$ = ${{12} \over {64}}$RZ2
$ \therefore $ ${{{\lambda _2}} \over {{\lambda _1}}}$ = ${5 \over {36}} \times {{64} \over {12}}$ = ${{20} \over {27}}$
$ \Rightarrow $ $\lambda $2 = ${{20} \over {27}}{\lambda _1}$
= ${{20} \over {27}}$ $ \times $ 6561 = 4860 $\mathop A\limits^o $ = 486 nm
2019
Q218
JEE Mains
MCQ
10 Mar 2026
Half lives of two radioactive nuclei A and B are 10 minutes and 20 minutes, respectively, If initially a sample
has equal number of nuclei, then after 60 minutes, the ratio of decayed numbers of nuclei A and B will be :
A.
9 : 8
B.
1 : 8
C.
8 : 1
D.
3 : 8
2019
Q219
JEE Mains
MCQ
10 Mar 2026
The electron in a hydrogen atom first jumps from the third excited state to the second excited state and
subsequently to the first excited state. The ratio of the respective wavelengths, ${{{\lambda _1}} \over {{\lambda _2}}}$, of the photons emitted
in this process is :
A.
${{22} \over 5}$
B.
${7 \over 5}$
C.
${9 \over 7}$
D.
${{20} \over 7}$
2019
Q220
JEE Mains
MCQ
10 Mar 2026
Consider an electron in a hydrogen atom revolving in its second excited state (having radius 4.65 $\mathop A\limits^o $). The
de-Broglie wavelength of this electron is :
A.
6.6 $\mathop A\limits^o $
B.
3.5 $\mathop A\limits^o $
C.
9.7 $\mathop A\limits^o $
D.
12.9 $\mathop A\limits^o $
2019
Q221
JEE Mains
MCQ
10 Mar 2026
An excited He+
ion emits two photons in succession, with wavelengths 108.5 nm and 30.4 nm, in making a
transition to ground state. The quantum number n, corresponding to its initial excited state is (for photon of
wavelength $\lambda $, energy $E = {{1240\,eV} \over {\lambda (in\,nm)}}$) :
A.
n = 4
B.
n = 7
C.
n = 5
D.
n = 6
2019
Q222
JEE Mains
MCQ
10 Mar 2026
In Li+ +, electron in first Bohr orbit is excited to a level by a radiation of wavelength $\lambda $. When the ion gets
deexcited to the ground state in all possible ways (including intermediate emissions), a total of six spectral
lines are observed. What is the value of $\lambda $?
(Given : H = 6.63 × 10–34 Js; c = 3 × 108 ms –1)
(Given : H = 6.63 × 10–34 Js; c = 3 × 108 ms –1)
A.
10.8 nm
B.
12.3 nm
C.
9.4 nm
D.
11.4 nm
${{hc} \over \lambda } = 13.6\,ev(g)\left\{ {1 - {1 \over {16}}} \right\}$
2019
Q223
JEE Mains
MCQ
10 Mar 2026
Two radioactive substances A and B have decay constants 5$\lambda $ and $\lambda $ respectively. At t = 0, a sample has the
same number of the two nuclei. The time taken for the ratio of the number of nuclei to become ${\left( {{1 \over e}} \right)^2}$
will be :
A.
${2 \over \lambda }$
B.
${1 \over {4\lambda }}$
C.
${1 \over {2\lambda }}$
D.
${1 \over {\lambda }}$
2019
Q224
JEE Mains
MCQ
10 Mar 2026
Two radioactive materials A and B have decay
constants 10$\lambda $ and $\lambda $, respectively. It initially
they have the same number of nuclei, then the
ratio of the number of nuclei of A to that of B
will be 1/e after a time :
A.
1/9$\lambda $
B.
11/10$\lambda $
C.
1/10$\lambda $
D.
1/11$\lambda $
2019
Q225
JEE Mains
MCQ
10 Mar 2026
A He+ ion is in its first excited state. Its
ionization energy is :-
A.
13.60 eV
B.
6.04 eV
C.
48.36 eV
D.
54.40 eV
2019
Q226
JEE Mains
MCQ
10 Mar 2026
Taking the wavelength of first Balmer line in
hydrogen spectrum (n = 3 to n = 2) as 660 nm,
the wavelength of the 2nd Balmer line (n = 4 to
n = 2) will be :
A.
642.7 nm
B.
488.9 nm
C.
889.2 nm
D.
388.9 nm
2019
Q227
JEE Mains
MCQ
10 Mar 2026
The ratio of mass densities of nuclei of 40Ca
and 16O is close to :-
A.
1
B.
5
C.
0.1
D.
2
2019
Q228
JEE Mains
MCQ
10 Mar 2026
Radiation coming from transitions
n = 2 to n = 1 of hydrogen atoms fall on He+
ions in n = 1 and n = 2 states. The possible
transition of helium ions as they absorb energy
from the radiation is :
A.
n = 1 $ \to $ n = 4
B.
n = 2 $ \to $ n = 5
C.
n = 2 $ \to $ n = 4
D.
n = 2 $ \to $ n = 3
2019
Q229
JEE Mains
MCQ
10 Mar 2026
In a radioactive decay chain, the initial nucleus is ${}_{90}^{232}$Th. At the end there are 6 $\alpha $-particles and 4 $\beta $-particles which are emitted. If the end nucleus is ${}_Z^A$X, A and Z are given by :
A.
A = 208; Z = 80
B.
A = 208; Z = 82
C.
A = 200; Z = 81
D.
A = 202; Z = 80
2019
Q230
JEE Mains
MCQ
10 Mar 2026
A particle of mass m moves in a circular orbit in a central potential field U(r) = ${1 \over 2}$ kr2. If Bohr 's
quantization conditions are applied, radii of possible orbitls and energy levels vary with quantum number n as :
A.
rn $ \propto $ $\sqrt n $, En $ \propto $ n
B.
rn $ \propto $ $\sqrt n $, En $ \propto $ ${1 \over n}$
C.
rn $ \propto $ n, En $ \propto $ n
D.
rn $ \propto $ n2, En $ \propto $ ${1 \over {{n^2}}}$
2019
Q231
JEE Mains
MCQ
10 Mar 2026
In a hydrogen like atom, when an electron jumps from the M-shell to the L-shell, the wavelength of emitted radiation is $\lambda $. If an electron jumps from N-shell to the L-shell, the wavelength of emitted radiation will be:
A.
${{25} \over {16}}$ $\lambda $
B.
${{27} \over {20}}$ $\lambda $
C.
${{16} \over {25}}$ $\lambda $
D.
${{20} \over {27}}$ $\lambda $
2019
Q232
JEE Mains
MCQ
10 Mar 2026
A hydrogen atom, initially in the ground state is excited by absorbing a photon of wavelength 980$\mathop A\limits^ \circ $. The radius of the atom in the excited state, in terms of Bohr radius a0 will be : (hc = 12500 eV$\mathop A\limits^ \circ $)
A.
4a0
B.
9a0
C.
25a0
D.
16a0
2019
Q233
JEE Mains
MCQ
10 Mar 2026
Consider the nuclear fission
Ne20 $ \to $ 2He4 + C12
Given that the binding energy/ nucleon of Ne20, He4 and C12 are, respectively, 8.03 MeV, 7.07 MeV and 7.86 MeV, identify the correct statement -
Ne20 $ \to $ 2He4 + C12
Given that the binding energy/ nucleon of Ne20, He4 and C12 are, respectively, 8.03 MeV, 7.07 MeV and 7.86 MeV, identify the correct statement -
A.
8.3 MeV energy will be released
B.
energy of 11.9 MeV has to be supplied
C.
energy of 12.4 MeV will be supplied
D.
energy of 3.6 MeV will be released
2019
Q234
JEE Mains
MCQ
10 Mar 2026
Using a nuclear counter the count rate of emitted particles from a radioactive source is measured. At t = 0 it was 1600 counts per second and t = 8 seconds it was 100 counts per second. The count rate observed, as counts per second, at t = 6 seconds is close to -
A.
200
B.
150
C.
400
D.
360
2019
Q235
JEE Mains
MCQ
10 Mar 2026
At a given instant, say t = 0, two radioactive substance A and B have equal activities. the ratio ${{{R_B}} \over {{R_A}}}$ of their activities after time t itself decays with time t as e$-$3t. If the half-life of A is ln2, the half-life of B is :
A.
4ln2
B.
${{\ln 2} \over 2}$
C.
${{\ln 2} \over 4}$
D.
2ln2
2019
Q236
JEE Mains
MCQ
10 Mar 2026
A sample of radioactive material A, that has an activity of 10 mCi(1 Ci = 3.7 $ \times $ 1010 decays/s), has twice the number of nuclei as another sample of a different radioactive materail B which has an activity of 20 mCi. The correct choices for half-lives of A and B would then be respectively :
A.
5 days and 10 days
B.
10 days and 40 days
C.
20 days and 5 days
D.
20 days and 10 days
2018
Q237
JEE Mains
MCQ
10 Mar 2026
At some instant, a radioactive sample S1 having an activity 5 $\mu $Ci has twice the number of nuclei as another sample S2 which has an activity of 10 $\mu $Ci. The half lives of S1 and S2 are :
A.
20 years and 5 years, respectively
B.
20 years and 10years, respectively
C.
5 years and 20 years, respectively
D.
10 years and 20 years, respectively
2018
Q238
JEE Mains
MCQ
10 Mar 2026
An electron from various excited states of hydrogen atom emit radiation to come to the ground state. Let
${\lambda _n}$, ${\lambda _g}$ be the de Broglie wavelength of the electron in the nth state and the ground state respectively. Let
${\Lambda _n}$ be the wavelength of the emitted photon in the transition from the nth state to the ground state. For large n, (A, B are constants)
A.
${\Lambda _n} \approx A + {B \over {\lambda _n^2}}$
B.
${\Lambda _n} \approx A + B{\lambda _n}$
C.
$\Lambda _n^2 \approx A + B\lambda _n^2$
D.
$\Lambda _n^2 \approx \lambda$
2018
Q239
JEE Mains
MCQ
10 Mar 2026
If the series limit frequency of the Lyman series is ${\nu _L}$, then the series limit frequency of the Pfund series is:
A.
${\nu _L}/25$
B.
$25{\nu _L}$
C.
$16{\nu _L}$
D.
${\nu _L}/16$
2018
Q240
JEE Mains
MCQ
10 Mar 2026
It is found that if a neutron suffers an elastic collinear collision with deuterium at rest, fractional loss of its
energy is pd; while for its similar collision with carbon nucleus at rest, fractional loss of energy is pc. The values of pd and pc are respectively :
A.
(0, 1)
B.
(0.89, 0.28)
C.
(0.28, 0.89)
D.
(0, 0)
2018
Q241
JEE Mains
MCQ
10 Mar 2026
Muon ($\mu $$-$) is a negatively charged (|q| = |e|) particle with a mass m$\mu $ = 200 me, where me is the mass of the electron and e is the electronic charge. If $\mu $$-$ is bond to a proton to form a hydrogen like atom, identify the correct statements.
(A) Radis of the muonic orbit is 200 times smaller than that of the electron.
(B) The speed of the $\mu $$-$ in the nth orbit is ${1 \over {200}}$ times that of the electron in the nth orbit.
(C) The ionization energy of muonic atom is 200 timesmore than of an hydroen atom.
(D) The momentum of the muon in the nth orbit is 200 times more than that of the electron.
(A) Radis of the muonic orbit is 200 times smaller than that of the electron.
(B) The speed of the $\mu $$-$ in the nth orbit is ${1 \over {200}}$ times that of the electron in the nth orbit.
(C) The ionization energy of muonic atom is 200 timesmore than of an hydroen atom.
(D) The momentum of the muon in the nth orbit is 200 times more than that of the electron.
A.
(A), (B), (D)
B.
(A), (C), (D)
C.
(B), (D)
D.
(C), (D)
2018
Q242
JEE Mains
MCQ
10 Mar 2026
An unstable heavy nucleus at rest breaks into two nuclei which move away with velocities in the ratio of 8 : 27. The ratio of the radii of the nuclei (assumed to be spherical) is :
A.
8 : 27
B.
4 : 9
C.
3 : 2
D.
2 : 3
2018
Q243
JEE Mains
MCQ
10 Mar 2026
The energy required to remove the electron from a singly ionized Helium atom is $2.2$ times the energies required to remove an electron from Helium atom. The total energy required to ionize the Helium atom completely is :
A.
$20$ $eV$
B.
$34$ $eV$
C.
$79$ $eV$
D.
$109$ $eV$
2018
Q244
JEE Mains
MCQ
10 Mar 2026
A solution containing active cobalt ${^{60}_{27}}Co$ having activity of $0.8$ $\mu Ci$ and decay constant $\lambda $ is injected in an animal's body. If $1\,c{m^3}$ of blood is drawn from the animal's body after $10$ hrs of injection, the activity found was $300$ decays per minute What is the volume of blood that is flowing in the body ? $\left( {\,\,Ci = 3.7 \times {{10}^{10}}\,} \right.$ decays per second and at $t=10$ hrs $\left. {{e^{ - \lambda t}} = 0.84} \right)$
A.
$6$ liters
B.
$7$ liters
C.
$4$ liters
D.
$5$ liters
2017
Q245
JEE Mains
MCQ
10 Mar 2026
The acceleration of an electron in the first orbit of the hydrogen atom (n = 1) is :
A.
${{{h^2}} \over {{\pi ^2}{m^2}{r^3}}}$
B.
${{{h^2}} \over {{8\pi ^2}{m^2}{r^3}}}$
C.
${{{h^2}} \over {{4\pi ^2}{m^2}{r^3}}}$
D.
${{{h^2}} \over {{4\pi }{m^2}{r^3}}}$
2017
Q246
JEE Mains
MCQ
10 Mar 2026
Imagine that a reactor converts all given mass into energy and that it operates at a power level of 109 watt. The mass of the fuel consumed per hour in the reactor will be : (velocity of light, c is
3×108 m/s)
A.
0.96 gm
B.
0.8 gm
C.
4 $ \times $ 10$-$2 gm
D.
6.6 $ \times $ 10$-$5 gm
2017
Q247
JEE Mains
MCQ
10 Mar 2026
Two deuterons undergo nuclear fusion to form a Helium nucleus. Energy released in this process is : (given binding energy per nucleon for deuteron = 1.1 MeV and for helium = 7.0 MeV)
A.
30.2 MeV
B.
32.4 MeV
C.
23.6 MeV
D.
25.8 MeV
2017
Q248
JEE Mains
MCQ
10 Mar 2026
According to Bohr’s theory, the time averaged magnetic field at the centre (i.e. nucleus) of a hydrogen atom due to the motion of electrons in the nth orbit is proportional to : (n = principal quantum number)
A.
${n^{ - 4}}$
B.
${n^{ - 5}}$
C.
n$-$3
D.
n$-$2
2017
Q249
JEE Mains
MCQ
10 Mar 2026
A radioactive nucleus A with a half life T, decays into a nucleus B. At t = 0, there is no nucleus B. At
sometime t, the ratio of the number of B to that of A is 0.3. Then, t is given by :
A.
$t = {T \over {\log (1.3)}}$
B.
$t = T\log (1.3)$
C.
$t = {T \over 2}{{\log 2} \over {\log 1.3}}$
D.
$t = T{{\log 1.3} \over {\log 2}}$
2017
Q250
JEE Mains
MCQ
10 Mar 2026
Some energy levels of a molecule are shown in the figure. The
ratio of the wavelengths r = ${{\lambda _1}}$/${{\lambda _2}}$, is given by:
A.
r = 1/3
B.
r = 4/3
C.
r = 2/3
D.
r = 3/4