Atoms and Nuclei
299 Questions
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 (Online) 19th April Morning Slot
Match List - I (Experiment performed) with List - II (Phenomena discovered/associated) and select the correct option from the options given below the lists :
| List - I | List - II | ||
|---|---|---|---|
| (a) | Davisson and Germer Experiment | (i) | Wave nature of electrons |
| (b) | Millikan’s oil drop experiment | (ii) | Charge of an electron |
| (c) | Rutherford experiment | (iii) | Quantisation of energy levels |
| (d) | Franck - Hertz experiment | (iv) | Existence of nucleus |
A.
(a)-(i), (b)-(ii), (c)-(iii), (d)-(iv)
B.
(a)-(i), (b)-(ii), (c)-(iv), (d)-(iii)
C.
(a)-(iii), (b)-(iv), (c)-(i), (d)-(ii)
D.
(a)-(iv), (b)-(iii), (c)-(ii), (d)-(i)
2014
JEE Mains
MCQ
JEE Main 2014 (Online) 19th April Morning Slot
A piece of wood from a recently cut tree shows 20 decays per minute. A wooden piece of same size placed in a museum (obtained from a tree cut many years back) shows 2 decays per minute. If half life of C14 is 5730 years, then age of the wooden piece placed in the museum is approximately :
A.
10439 years
B.
13094 years
C.
19039 years
D.
39049 years
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
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- 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.
${T_n} \propto {1 \over n},{r_n} \propto {n^2}$
2007
JEE Mains
MCQ
AIEEE 2007
The half-life period of a ratio-active element $X$ is same as the mean life time of another ratio-active element $Y.$ Initially they have the same number of atoms. Then
A.
$X$ and $Y$ decay at same rate always
B.
$X$ will decay faster than $Y$
C.
$Y$ will decay faster than $X$
D.
$X$ and $Y$ have same decay rate initially
2007
JEE Mains
MCQ
AIEEE 2007
Which of the following transitions in hydrogen atoms emit photons of highest frequency ?
A.
$n = 1$ to $n=2$
B.
$n = 2$ to $n=6$
C.
$n = 6$ to $n=2$
D.
$n = 2$ to $n=1$
2007
JEE Mains
MCQ
AIEEE 2007
In gamma ray emission from a nucleus
A.
only the proton number changes
B.
both the neutron number and the proton number change
C.
there is no change in the proton number and the neutron number
D.
only the neutron number changes
2007
JEE Mains
MCQ
AIEEE 2007
If ${M_O}$ is the mass of an oxygen isotope ${}_8{O^{17}}$ , ${M_p}$ and ${M_N}$ are the masses of a proton and neutron respectively, the nuclear binding energy of the isotope is
A.
$\left( {{M_O} - 17{M_N}} \right){C^2}$
B.
$\left( {{M_O} - 8{M_P}} \right){C^2}$
C.
$\left( {{M_O} - 8{M_P} - 9{M_N}} \right){C^2}$
D.
${{M_O}{c^2}}$
2006
JEE Mains
MCQ
AIEEE 2006
An alpha nucleus of energy ${1 \over 2}m{v^2}$ bombards a heavy nuclear target of charge $Ze$. Then the distance of closest approach for the alpha nucleus will be proportional to
A.
${v^2}$
B.
${1 \over m}$
C.
${1 \over {{v^2}}}$
D.
${1 \over {Ze}}$
2006
JEE Mains
MCQ
AIEEE 2006
The energy spectrum of $\beta $-particles [ number $N(E)$ as a function of $\beta $-energy $E$ ] emitted from a radioactive source is
A.
B.
C.
D.
2006
JEE Mains
MCQ
AIEEE 2006
The $'rad'$ is the correct unit used to report the measurement of
A.
the ability of a beam of gamma ray photons to produce ions in a target
B.
the energy delivered by radiation to a target
C.
the biological effect of radiation
D.
the rate of decay of radioactive source
2006
JEE Mains
MCQ
AIEEE 2006
When ${}_3L{i^7}$ nuclei are bombarded by protons, and the resultant nuclei are ${}_4B{e^8}$, the emitted particles will be
A.
alpha particles
B.
beta particles
C.
gamma photons
D.
neutrons
2006
JEE Mains
MCQ
AIEEE 2006
If the binding energy per nucleon in ${}_3^7Li$ and ${}_2^4He$ nuclei are $5.60$ $MeV$ and $7.06$ $MeV$ respectively, then in the reaction
$$p + {}_3^7Li \to 2\,{}_2^4He$$
energy of proton must be
energy of proton must be
A.
$28.24$ $MeV$
B.
$17.28$ $MeV$
C.
$1.46$ $MeV$
D.
$39.2$ $MeV$
2005
JEE Mains
MCQ
AIEEE 2005
The intensity of gamma radiation from a given source is $L$. On passing through $36$ $mm$ of lead, it is reduced to ${{\rm I} \over 8}.$ The thickness of lead which will reduce the intensity to ${{\rm I} \over 2}$ will be
A.
$9mm$
B.
$6mm$
C.
$12mm$
D.
$18mm$
2005
JEE Mains
MCQ
AIEEE 2005
The diagram shows the energy levels for an electron in a certain atom. Which transition shown represents the emission of a photon with the most energy?
A.
$iv$
B.
$iii$
C.
$ii$
D.
$i$
2005
JEE Mains
MCQ
AIEEE 2005
Starting with a sample of pure ${}^{66}Cu,{7 \over 8}$ of it decays into $Zn$ in $15$ minutes. The corresponding half life is
A.
$15$ minutes
B.
$10$ minutes
C.
$7{1 \over 2}$ minutes
D.
$5$ minutes
2005
JEE Mains
MCQ
AIEEE 2005
A nuclear transformation is denoted by $X\left( {n,\alpha } \right)\matrix{
7 \cr
3 \cr
} Li.$ Which of the following is the nucleus of element $X$ ?
A.
${}_5^{10}B$
B.
${}^{12}{C_6}$
C.
${}_4^{11}Be$
D.
${}_5^9B$
2005
JEE Mains
MCQ
AIEEE 2005
If radius of the $\matrix{
{27} \cr
{13} \cr
} $ $Al$ nucleus is estimated to be $3.6$ fermi then the radius of $\matrix{
{125} \cr
{52} \cr
} \,Te$ nucleus is estimated to be nearly
A.
$8$ fermi
B.
$6$ fermi
C.
$5$ fermi
D.
$4$ fermi
2004
JEE Mains
MCQ
AIEEE 2004
A nucleus disintegrated into two nuclear parts which have their velocities in the ratio of $2:1.$ The ratio of their nuclear sizes will be
A.
${3^{{\raise0.5ex\hbox{$\scriptstyle 1$}
\kern-0.1em/\kern-0.15em
\lower0.25ex\hbox{$\scriptstyle 2$}}}}:1$
B.
$1:{2^{1/3}}$
C.
${2^{1/3}}:1$
D.
$1:{3^{{\raise0.5ex\hbox{$\scriptstyle 1$}
\kern-0.1em/\kern-0.15em
\lower0.25ex\hbox{$\scriptstyle 2$}}}}$
2004
JEE Mains
MCQ
AIEEE 2004
The binding energy per nucleon of deuteron $\left( {{}_1^2\,H} \right)$ and helium nucleus $\left( {{}_2^4\,He} \right)$ is $1.1$ $MeV$ and $7$ $MeV$ respectively. If two deuteron nuclei react to form a single helium nucleus, then the energy released is
A.
$23.6\,\,MeV$
B.
$26.9\,\,MeV$
C.
$13.9\,\,MeV$
D.
$19.2\,\,MeV$
2004
JEE Mains
MCQ
AIEEE 2004
An $\alpha $-particle of energy $5$ $MeV$ is scattered through ${180^ \circ }$ by a fixed uranium nucleus. The distance of closest approach is of the order of
A.
${10^{ - 12}}\,cm$
B.
${10^{ - 10}}\,cm$
C.
$1A$
D.
${10^{ - 15a}}\,cm$
2003
JEE Mains
MCQ
AIEEE 2003
In the nuclear fusion reaction
$${}_1^2H + {}_1^3H \to {}_2^4He + n$$
given that the repulsive potential energy between the two nuclei is $ \sim 7.7 \times {10^{ - 14}}J$, the temperature at which the gases must be heated to initiate the reaction is nearly
[ Boltzmann's Constant $k = 1.38 \times {10^{ - 23}}\,J/K$ ]
given that the repulsive potential energy between the two nuclei is $ \sim 7.7 \times {10^{ - 14}}J$, the temperature at which the gases must be heated to initiate the reaction is nearly
[ Boltzmann's Constant $k = 1.38 \times {10^{ - 23}}\,J/K$ ]
A.
${10^7}\,\,K$
B.
${10^5}\,\,K$
C.
${10^3}\,\,K$
D.
${10^9}\,\,K$
2003
JEE Mains
MCQ
AIEEE 2003
Which of the following cannot be emitted by radioactive substances during their decay ?
A.
Protons
B.
Neutrinoes
C.
Helium nuclei
D.
Electrons
2003
JEE Mains
MCQ
AIEEE 2003
A radioactive sample at any instant has its disintegration rate $5000$ disintegrations per minute. After $5$ minutes, the rate is $1250$ disintegrations per minute. Then, the decay constant (per minute) is
A.
$0.4$ $ln2$
B.
$0.2$ $ln2$
C.
$0.1$ $ln2$
D.
$0.8$ $ln2$
2003
JEE Mains
MCQ
AIEEE 2003
If the binding energy of the electron in a hydrogen atom is $13.6eV,$ the energy required to remove the electron from the first excited state of $L{i^{ + + }}$ is
A.
$30.6$ $eV$
B.
$13.6$ $eV$
C.
$3.4$ $eV$
D.
$122.4$ $eV$
2003
JEE Mains
MCQ
AIEEE 2003
Which of the following atoms has the lowest ionization potential ?
A.
${}_7^{14}N$
B.
${}_{55}^{133}\,Cs$
C.
${}_{18}^{40}\,Ar$
D.
${}_8^{16}\,O$
2003
JEE Mains
MCQ
AIEEE 2003
Which of the following radiations has the least wavelength ?
A.
$\gamma $ - rays
B.
$\beta $ - rays
C.
$\alpha $ - rays
D.
$X$ - rays
2003
JEE Mains
MCQ
AIEEE 2003
The wavelengths involved in the spectrum of deuterium $\left( {{}_1^2\,D} \right)$ are slightly different from that of hydrogen spectrum, because
A.
the size of the two nuclei are different
B.
the nuclear forces are different in the two cases
C.
the masses of the two nuclei are different
D.
the attraction between the electron and the nucleus is different in the two cases
2003
JEE Mains
MCQ
AIEEE 2003
A nucleus with $Z=92$ emits the following in a sequence:
$$\alpha ,{\beta ^ - },{\beta ^ - },\alpha ,\alpha ,\alpha ,\alpha ,\alpha ,{\beta ^ - },{\beta ^ - },\alpha ,{\beta ^ + },{\beta ^ + },\alpha $$
Then $Z$ of the resulting nucleus is
A.
$76$
B.
$78$
C.
$82$
D.
$74$
2003
JEE Mains
MCQ
AIEEE 2003
When a ${U^{238}}$ nucleus originally at rest, decays by emitting an alpha particle having a speed $'u',$ the recoil speed of the residual nucleus is
A.
${{4\mu } \over {238}}$
B.
$ - {{4\mu } \over {234}}$
C.
$ {{4\mu } \over {234}}$
D.
$ - {{4\mu } \over {238}}$
2002
JEE Mains
MCQ
AIEEE 2002
At a specific instant emission of radioactive compound is deflected in a magnetic field. The compound can emit
$\eqalign{ & \left( i \right)\,\,\,\,\,\,\,electrons\,\,\,\,\,\,\,\,\,\,\,\,\left( {ii} \right)\,\,\,\,\,\,\,protons \cr & \left( {iii} \right)\,\,\,H{e^{2 + }}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( {iv} \right)\,\,\,\,\,\,\,neutrons \cr} $
$\eqalign{ & \left( i \right)\,\,\,\,\,\,\,electrons\,\,\,\,\,\,\,\,\,\,\,\,\left( {ii} \right)\,\,\,\,\,\,\,protons \cr & \left( {iii} \right)\,\,\,H{e^{2 + }}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( {iv} \right)\,\,\,\,\,\,\,neutrons \cr} $
The emission at instant can be
A.
$i, ii, iii$
B.
$i, ii, iii, iv$
C.
$iv$
D.
$ii, iii$
2002
JEE Mains
MCQ
AIEEE 2002
If $13.6$ $eV$ energy is required to ionize the hydrogen atom, then the energy required to remove an electron from $n=2$ is
A.
$10.2$ $eV$
B.
$0$ $eV$
C.
$3.4$ $eV$
D.
$6.8$ $eV.$
2002
JEE Mains
MCQ
AIEEE 2002
If ${N_0}$ is the original mass of the substance of half-life period ${t_{1/2}} = 5$ years, then the amount of substance left after $15$ years is
A.
${N_0}/8$
B.
${N_0}/16$
C.
${N_0}/2$
D.
${N_0}/4$