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Atoms and Nuclei

345 Questions
All Exams JEE Mains JEE Advanced
2019 JEE Mains MCQ
JEE Main 2019 (Online) 12th April Evening Slot
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 JEE Mains MCQ
JEE Main 2019 (Online) 12th April Evening Slot
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 JEE Mains MCQ
JEE Main 2019 (Online) 12th April Morning Slot
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 JEE Mains MCQ
JEE Main 2019 (Online) 10th April Evening Slot
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 $?
(Given : H = 6.63 × 10–34 Js; c = 3 × 108 ms –1)
A.
10.8 nm
B.
12.3 nm
C.
9.4 nm
D.
11.4 nm
2019 JEE Mains MCQ
JEE Main 2019 (Online) 10th April Evening Slot
Two radioactive substances A and B have decay constants 5$\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 JEE Mains MCQ
JEE Main 2019 (Online) 10th April Morning Slot
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 JEE Mains MCQ
JEE Main 2019 (Online) 9th April Evening Slot
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 JEE Mains MCQ
JEE Main 2019 (Online) 9th April Morning Slot
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 JEE Mains MCQ
JEE Main 2019 (Online) 8th April Evening Slot
The ratio of mass densities of nuclei of 40Ca and 16O is close to :-
A.
1
B.
5
C.
0.1
D.
2
2019 JEE Mains MCQ
JEE Main 2019 (Online) 8th April Morning Slot
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 JEE Mains MCQ
JEE Main 2019 (Online) 12th January Evening Slot
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 JEE Mains MCQ
JEE Main 2019 (Online) 12th January Morning Slot
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 JEE Mains MCQ
JEE Main 2019 (Online) 11th January Evening Slot
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 JEE Mains MCQ
JEE Main 2019 (Online) 11th January Morning Slot
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 JEE Mains MCQ
JEE Main 2019 (Online) 10th January Evening Slot
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 -
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 JEE Mains MCQ
JEE Main 2019 (Online) 10th January Morning Slot
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 JEE Mains MCQ
JEE Main 2019 (Online) 9th January Evening Slot
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 JEE Mains MCQ
JEE Main 2019 (Online) 9th January Morning Slot
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 JEE Mains MCQ
JEE Main 2018 (Online) 16th April Morning Slot
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 JEE Mains MCQ
JEE Main 2018 (Offline)
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 JEE Mains MCQ
JEE Main 2018 (Offline)
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 JEE Mains MCQ
JEE Main 2018 (Offline)
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 JEE Mains MCQ
JEE Main 2018 (Online) 15th April Evening Slot
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.
(A),    (B),    (D)
B.
(A),    (C),    (D)
C.
(B),    (D)
D.
(C),    (D)
2018 JEE Mains MCQ
JEE Main 2018 (Online) 15th April Evening Slot
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 JEE Mains MCQ
JEE Main 2018 (Online) 15th April Morning Slot
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 JEE Mains MCQ
JEE Main 2018 (Online) 15th April Morning Slot
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 JEE Mains MCQ
JEE Main 2017 (Online) 9th April Morning Slot
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 JEE Mains MCQ
JEE Main 2017 (Online) 9th April Morning Slot
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 JEE Mains MCQ
JEE Main 2017 (Online) 8th April Morning Slot
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 JEE Mains MCQ
JEE Main 2017 (Online) 8th April Morning Slot
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 JEE Mains MCQ
JEE Main 2017 (Offline)
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 JEE Mains MCQ
JEE Main 2017 (Offline)
Some energy levels of a molecule are shown in the figure. The ratio of the wavelengths r = ${{\lambda _1}}$/${{\lambda _2}}$, is given by:

JEE Main 2017 (Offline) Physics - Atoms and Nuclei Question 240 English
A.
r = 1/3
B.
r = 4/3
C.
r = 2/3
D.
r = 3/4
2016 JEE Mains MCQ
JEE Main 2016 (Online) 9th April Morning Slot
A hydrogen atom makes a transition from n = 2 to n = 1 and emits a photon. This photon strikes a doubly ionized lithium atom (z = 3) in excited state and completely removes the orbiting electron. The least quantum number for the excited state of the ion for the process is :
A.
2
B.
3
C.
4
D.
5
2016 JEE Mains MCQ
JEE Main 2016 (Offline)
Half-lives of two radioactive elements $A$ and $B$ are $20$ minutes and $40$ minutes, respectively. Initially, the samples have equal number of nuclei. After $80$ minutes, the ratio of decayed number of $A$ and $B$ nuclei will be:
A.
$1:4$
B.
$5:4$
C.
$1:16$
D.
$4:1$
2015 JEE Mains MCQ
JEE Main 2015 (Offline)
As an electron makes a transition from an excited state to the ground state of a hydrogen - like atom/ion :
A.
kinetic energy decreases, potential energy increases but total energy remains same
B.
kinetic energy and total energy decrease but potential energy increases
C.
its kinetic energy increases but potential energy and total energy decrease
D.
kinetic energy, potential energy and total energy decrease
2014 JEE Mains MCQ
JEE Main 2014 (Offline)
The radiation corresponding to $3 \to 2$ transition of hydrogen atom falls on a metal surface to produce photoelectrons. These electrons are made to enter a magnetic field $3 \times {10^{ - 4}}\,T.$ If the radius of the larger circular path followed by these electrons is $10.0$ $mm$, the work function of the metal is close to:
A.
$1.8$ $eV$
B.
$1.1$ $eV$
C.
$0.8$ $eV$
D.
$1.6$ $eV$
2014 JEE Mains MCQ
JEE Main 2014 (Offline)
Hydrogen $\left( {{}_1{H^1}} \right)$, Deuterium $\left( {{}_1{H^2}} \right)$, singly ionised Helium ${\left( {{}_2H{e^4}} \right)^ + }$ and doubly ionised lithium ${\left( {{}_3L{i^6}} \right)^{ + + }}$ all have one electron around the nucleus. Consider an electron transition from $n=2$ to $n=1.$ If the wavelengths of emitted radiation are ${\lambda _1},{\lambda _2},{\lambda _3}$ and ${\lambda _4}$ respectively then approximately which one of the following is correct?
A.
$4{\lambda _1} = 2{\lambda _2} = 2{\lambda _3} = {\lambda _4}$
B.
${\lambda _1} = 2{\lambda _2} = 2{\lambda _3} = {\lambda _4}$
C.
${\lambda _1} = {\lambda _2} = 4{\lambda _3} = 9{\lambda _4}$
D.
${\lambda _1} = 2{\lambda _2} = 3{\lambda _3} = 4{\lambda _4}$
2013 JEE Mains MCQ
JEE Main 2013 (Offline)
In a hydrogen like atom electron make transition from an energy level with quantum number $n$ to another with quantum number $\left( {n - 1} \right)$. If $n > > 1,$ the frequency of radiation emitted is proportional to :
A.
${1 \over n}$
B.
${1 \over {{n^2}}}$
C.
${1 \over {{n^{{3 \over 2}}}}}$
D.
${1 \over {{n^3}}}$
2012 JEE Mains MCQ
AIEEE 2012
Assume that a neutron breaks into a proton and an electron. The energy released during this process is : (mass of neutron $ = 1.6725 \times {10^{ - 27}}kg,$ mass of proton $ = 1.6725 \times {10^{ - 27}}\,kg,$ mass of electron $ = 9 \times {10^{ - 31}}\,kg$ ).
A.
$0.51$ $MeV$
B.
$7.10\,MeV$
C.
$6.30\,MeV$
D.
$5.4\,MeV$
2012 JEE Mains MCQ
AIEEE 2012
A diatomic molecule is made of two masses ${m_1}$ and ${m_2}$ which are separated by a distance $r.$ If we calculate its rotational energy by applying Bohr's rule of angular momentum quantization, its energy will be given by: ($n$ is an integer)
A.
${{{{\left( {{m_1} + {m_2}} \right)}^2}{n^2}{h^2}} \over {2m_1^2m_2^2{r^2}}}$
B.
${{{n^2}{h^2}} \over {2\left( {{m_1} + {m_2}} \right){r^2}}}$
C.
${{2{n^2}{h^2}} \over {\left( {{m_1} + {m_2}} \right){r^2}}}$
D.
${{\left( {{m_1} + {m_2}} \right){n^2}{h^2}} \over {2{m_1}{m_2}{r^2}}}$
2012 JEE Mains MCQ
AIEEE 2012
Hydrogen atom is excited from ground state to another state with principal quantum number equal to $4.$ Then the number of spectral lines in the emission spectra will be :
A.
$2$
B.
$3$
C.
$5$
D.
$6$
2011 JEE Mains MCQ
AIEEE 2011
Energy required for the electron excitation in $L{i^{ + + }}$ from the first to the third Bohr orbit is :
A.
$36.3$ $eV$
B.
$108.8$ $eV$
C.
$122.4$ $eV$
D.
$12.1$ $eV$
2011 JEE Mains MCQ
AIEEE 2011
The half life of a radioactive substance is $20$ minutes. The approximate time interval $\left( {{t_2} - {t_1}} \right)$ between the time ${{t_2}}$ when ${2 \over 3}$ of it had decayed and time ${{t_1}}$ when ${1 \over 3}$ of it had decayed is :
A.
$14$ min
B.
$20$ min
C.
$28$ min
D.
$7$ min
2010 JEE Mains MCQ
AIEEE 2010
A nucleus of mass $M+$$\Delta m$ is at rest and decays into two daughter nuclei of equal mass ${M \over 2}$ each. Speed of light is $c.$

The binding energy per nucleon for the parent nucleus is ${E_1}$ and that for the daughter nuclei is ${E_2}.$ Then

A.
${E_2} = 2{E_1}$
B.
${E_1} > {E_2}$
C.
${E_2} > {E_1}$
D.
${E_1} = 2{E_2}$
2010 JEE Mains MCQ
AIEEE 2010
A radioactive nucleus (initial mass number $A$ and atomic number $Z$ emits $3\,\alpha $- particles and $2$ positrons. The ratio of number of neutrons to that of protons in the final nucleus will be
A.
${{A - Z - 8} \over {Z - 4}}$
B.
${{A - Z - 4} \over {Z - 8}}$
C.
${{A - Z - 12} \over {Z - 4}}$
D.
${{A - Z - 4} \over {Z - 2}}$
2010 JEE Mains MCQ
AIEEE 2010
A nucleus of mass $M+$$\Delta m$ is at rest and decays into two daughter nuclei of equal mass ${M \over 2}$ each. Speed of light is $c.$

The speed of daughter nuclei is

A.
$c{{\Delta m} \over {M + \Delta m}}$
B.
$c\sqrt {{{2\Delta m} \over M}} $
C.
$c\sqrt {{{\Delta m} \over M}} $
D.
$c\sqrt {{{\Delta m} \over {M + \Delta m}}} $
2009 JEE Mains MCQ
AIEEE 2009
The transition from the state $n=4$ to $n=3$ in a hydrogen like atom result in ultra violet radiation. Infrared radiation will be obtained in the transition from :
A.
$3 \to 2$
B.
$4 \to 2$
C.
$5 \to 4$
D.
$2 \to 1$
2009 JEE Mains MCQ
AIEEE 2009
AIEEE 2009 Physics - Atoms and Nuclei Question 244 English

The above is a plot of binding energy per nucleon ${E_b},$ against the nuclear mass $M;A,B,C,D,E,F$ correspond to different nuclei. Consider four reactions :
$\eqalign{ & \left( i \right)\,\,\,\,\,\,\,\,\,\,A + B \to C + \varepsilon \,\,\,\,\,\,\,\,\,\,\left( {ii} \right)\,\,\,\,\,\,\,\,\,\,C \to A + B + \varepsilon \,\,\,\,\,\,\,\,\,\, \cr & \left( {iii} \right)\,\,\,\,\,\,D + E \to F + \varepsilon \,\,\,\,\,\,\,\,\,\,\left( {iv} \right)\,\,\,\,\,\,\,\,\,F \to D + E + \varepsilon ,\,\,\,\,\,\,\,\,\,\, \cr} $

where $\varepsilon $ is the energy released? In which reactions is $\varepsilon $ positive?

A.
$(i)$ and $(iii)$
B.
$(ii)$ and $(iv)$
C.
$(ii)$ and $(iii)$
D.
$(i)$ and $(iv)$
2008 JEE Mains MCQ
AIEEE 2008
This question contains Statement- 1 and Statement- 2. Of the four choices given after the statements, choose the one that best describes the two statements:
Statement- 1:
Energy is released when heavy nuclei undergo fission or light nuclei undergo fusion and

Statement- 2:
For heavy nuclei, binding energy per nucleon increases with increasing $Z$ while for light nuclei it decreases with increasing $Z.$

A.
Statement - $1$ is false, Statement - $2$ is true
B.
Statement - $1$ is true, Statement - $2$ is true; Statement - $2$ is a correct explanation for Statement - $1$
C.
Statement - $1$ is true, Statement - $2$ is true; Statement - $2$ is not a correct explanation for Statement - $1$
D.
Statement - $1$ is true, Statement - $2$ is false
2008 JEE Mains MCQ
AIEEE 2008
Suppose an electron is attracted towards the origin by a force ${k \over r}$ where $'k'$ is a constant and $'r'$ is the distance of the electron from the origin. By applying Bohr model to this system, the radius of the ${n^{th}}$ orbital of the electron is found to be $'{r_n}'$ and the kinetic energy of the electron to be $'{T_n}'.$

Then which of the following is true?

A.
${T_n} \propto {1 \over {{n^2}}},{r_n} \propto {n^2}$
B.
${T_n}$ independent of $n,{r_n} \propto n$
C.
${T_n} \propto {1 \over n},{r_n} \propto n$
D.
${T_n} \propto {1 \over n},{r_n} \propto {n^2}$