Dual Nature, Atoms & Nuclei · JEE Main previous year questions

2024 40 questions

1. Q502024 · 9 Apr 2024 · Shift 1

   A proton, an electron and an alpha particle have the same energies. Their de-Broglie wavelengths will be compared as :

   1. A.${\lambda }_{\mathrm{p}}>{\lambda }_{\mathrm{e}}>{\lambda }_{\alpha }$
   2. B.${\lambda }_{\alpha }<{\lambda }_{\mathrm{p}}<{\lambda }_{\mathrm{e}}$
   3. C.${\lambda }_{\mathrm{e}}>{\lambda }_{\alpha }>{\lambda }_{\mathrm{p}}$
   4. D.${\lambda }_{\mathrm{p}}<{\lambda }_{\mathrm{e}}<{\lambda }_{\alpha }$
   Show answer

   Answer: B

2. Q342024 · 9 Apr 2024 · Shift 2

   A nucleus at rest disintegrates into two smaller nuclei with their masses in the ratio of $2:1$. After disintegration they will move :

   1. A.in opposite directions with speed in the ratio of $1:2$ respectively.
   2. B.in the same direction with same speed.
   3. C.in opposite directions with speed in the ratio of $2:1$ respectively.
   4. D.in opposite directions with the same speed.
   Show answer

   Answer: A

3. Q412024 · 9 Apr 2024 · Shift 2

   The energy released in the fusion of $2\mathrm{kg}$ of hydrogen deep in the sun is $E_H$ and the energy released in the fission of $2\mathrm{kg}$ of ${}^{235}\mathrm{U}$ is $E_U$. The ratio $\frac{E_H}{E_U}$ is approximately: (Consider the fusion reaction as $4{}_1^1\mathrm{H}+2{\mathrm{e}}^{-}\to {}_2^4\mathrm{He}+2\nu +6\gamma +26.7\mathrm{MeV}$, energy released in the fission reaction of ${}^{235}\mathrm{U}$ is $200\mathrm{MeV}$ per fission nucleus and ${\mathrm{N}}_{\mathrm{A}}=6.023\times 10^{23}$)

   1. A.7.62
   2. B.25.6
   3. C.9.13
   4. D.15.04
   Show answer

   Answer: A

4. Q422024 · 9 Apr 2024 · Shift 2

   A hydrogen atom in ground state is given an energy of $10.2\mathrm{eV}$. How many spectral lines will be emitted due to transition of electrons?

   1. A.3
   2. B.6
   3. C.10
   4. D.1
   Show answer

   Answer: D

5. Q462024 · 8 Apr 2024 · Shift 1

   A proton and an electron are associated with same de-Broglie wavelength. The ratio of their kinetic energies is: (Assume $h=6.63\times 10^{-34}\text{ J s},m_e=9.0\times 10^{-31}\text{ kg}$ and $m_p=1836\text{ times }{m}_e$)

   1. A.$1:\frac{1}{1836}$
   2. B.$1:\sqrt{1836}$
   3. C.$1:1836$
   4. D.$1:\frac{1}{\sqrt{1836}}$
   Show answer

   Answer: C

6. Q482024 · 8 Apr 2024 · Shift 1

   Binding energy of a certain nucleus is $18\times 10^8\text{ J}$. How much is the difference between total mass of all the nucleons and nuclear mass of the given nucleus:

   1. A.$20\mu \text{g}$
   2. B.$2\mu \text{g}$
   3. C.$10\mu \text{g}$
   4. D.$0.2\mu \text{g}$
   Show answer

   Answer: A

7. Q602024 · 8 Apr 2024 · Shift 1· Numerical answer

   In an alpha particle scattering experiment distance of closest approach for the $\alpha$ particle is $4.5\times 10^{-14}\text{ m}$. If target nucleus has atomic number 80 , then maximum velocity of $\alpha$-particle is ________ $\times 10^5\text{ m/s}$ approximately. ($\frac{1}{4\pi {ϵ}_0}=9\times 10^9\text{ SI unit}$, mass of $\alpha$ particle $=6.72\times 10^{-27}\text{ kg}$)

   Show answer

   Answer: 156

8. Q382024 · 8 Apr 2024 · Shift 2

   If $M_0$ is the mass of isotope ${}_5^{12}\mathrm{B}$, $M_p$ and $M_n$ are the masses of proton and neutron, then nuclear binding energy of isotope is:

   1. A.$(5M_p+7M_n-M_0)C^2$
   2. B.$(M_0-5M_p-7M_n)C^2$
   3. C.$(M_0-5M_p)C^2$
   4. D.$(M_0-12M_n)C^2$
   Show answer

   Answer: A

9. Q462024 · 8 Apr 2024 · Shift 2

   A proton and an electron have the same de Broglie wavelength. If ${\mathrm{K}}_{\mathrm{p}}$ and ${\mathrm{K}}_{\mathrm{e}}$ be the kinetic energies of proton and electron respectively, then choose the correct relation :

   1. A.${\mathrm{K}}_{\mathrm{p}}>{\mathrm{K}}_{\mathrm{e}}$
   2. B.${\mathrm{K}}_{\mathrm{p}}={\mathrm{K}}_{\mathrm{e}}$
   3. C.${\mathrm{K}}_{\mathrm{p}}<{\mathrm{K}}_{\mathrm{e}}$
   4. D.${\mathrm{K}}_{\mathrm{p}}={{\mathrm{K}}_{\mathrm{e}}}^2$
   Show answer

   Answer: C

10. Q472024 · 8 Apr 2024 · Shift 2

    In a hypothetical fission reaction $${}_{92}{X}^{236}\to {}_{56}{Y}^{141}+{}_{36}{Z}^{92}+3R$$ The identity of emitted particles (R) is :

    1. A.Proton
    2. B.Neutron
    3. C.Electron
    4. D.$\gamma$-radiations
    Show answer

    Answer: B

11. Q402024 · 6 Apr 2024 · Shift 2

    When UV light of wavelength $300\mathrm{nm}$ is incident on the metal surface having work function $2.13\mathrm{eV}$, electron emission takes place. The stopping potential is : (Given $\mathrm{hc}=1240\mathrm{eV}\mathrm{nm}$ )

    1. A.$4\mathrm{V}$
    2. B.$2\mathrm{V}$
    3. C.$4.1\mathrm{V}$
    4. D.$1.5\mathrm{V}$
    Show answer

    Answer: B

12. Q592024 · 6 Apr 2024 · Shift 2· Numerical answer

    In Franck-Hertz experiment, the first dip in the current-voltage graph for hydrogen is observed at $10.2\text{ V}$. The wavelength of light emitted by hydrogen atom when excited to the first excitation level is ________ $\text{nm}$. (Given $hc=1245\text{ eV nm},e=1.6\times 10^{-19}\text{ C}$).

    Show answer

    Answer: 122

13. Q392024 · 5 Apr 2024 · Shift 2

    Which of the following statement is not true about stopping potential $(V_0)$ ?

    1. A.It depends upon frequency of the incident light.
    2. B.It is $1/e$ times the maximum kinetic energy of electrons emitted.
    3. C.It increases with increase in intensity of the incident light.
    4. D.It depends on the nature of emitter material.
    Show answer

    Answer: C

14. Q572024 · 5 Apr 2024 · Shift 2· Numerical answer

    The shortest wavelength of the spectral lines in the Lyman series of hydrogen spectrum is $915\mathring{\mathrm{A}}$. The longest wavelength of spectral lines in the Balmer series will be ____ $\mathring{\mathrm{A}}$.

    Show answer

    Answer: 6588

15. Q382024 · 4 Apr 2024 · Shift 1

    Which of the following nuclear fragments corresponding to nuclear fission between neutron (${}_0^1\mathrm{n}$) and uranium isotope (${}_{92}^{235}\mathrm{U}$) is correct :

    1. A.${}_{56}^{140}\mathrm{Xe}+{}_{38}^{94}\mathrm{Sr}+3{}_0^1\mathrm{n}$
    2. B.${}_{51}^{153}\mathrm{Sb}+{}_{41}^{99}\mathrm{Nb}+3{}_0^1\mathrm{n}$
    3. C.${}_{56}^{144}\mathrm{Ba}+{}_{36}^{89}\mathrm{Kr}+4{}_0^1\mathrm{n}$
    4. D.${}_{56}^{144}\mathrm{Ba}+{}_{36}^{89}\mathrm{Kr}+3{}_0^1\mathrm{n}$
    Show answer

    Answer: D

16. Q432024 · 4 Apr 2024 · Shift 1
    
    1. A.
    2. B.
    3. C.
    4. D.
    Show answer

    Answer: C

17. Q532024 · 4 Apr 2024 · Shift 1· Numerical answer

    A hydrogen atom changes its state from $n=3$ to $n=2$. Due to recoil, the percentage change in the wavelength of emitted light is approximately $1\times 10^{-n}$. The value of $n$ is ____. [Given $\mathrm{Rhc}=13.6\mathrm{eV},\mathrm{hc}=1242\mathrm{eV}\mathrm{nm},\mathrm{h}=6.6\times 10^{-34}\mathrm{J}\mathrm{s}$ mass of the hydrogen atom $=1.6\times 10^{-27}\mathrm{kg}$]

    Show answer

    Answer: 7

18. Q402024 · 4 Apr 2024 · Shift 2

    According to Bohr's theory, the moment of momentum of an electron revolving in $4^{\text{th}}$ orbit of hydrogen atom is:

    1. A.$2\frac{h}{\pi }$
    2. B.$\frac{h}{2\pi }$
    3. C.$\frac{h}{\pi }$
    4. D.$8\frac{h}{\pi }$
    Show answer

    Answer: A

19. Q552024 · 4 Apr 2024 · Shift 2· Numerical answer

    The disintegration energy $Q$ for the nuclear fission of ${}^{235}\text{U}\to {}^{140}\text{Ce}+{}^{94}\text{Zr}+n$ is ________ $\text{MeV}$. Given atomic masses of ${}^{235}\text{U}:235.0439u$; ${}^{140}\text{Ce}:139.9054u$, ${}^{94}\text{Zr}:93.9063u$; $n:1.0086u$, Value of $c^2=931\text{ MeV}/u$.

    Show answer

    Answer: 208

20. Q402024 · 1 Feb 2024 · Shift 1

    The minimum energy required by a hydrogen atom in ground state to emit radiation in Balmer series is nearly :

    1. A.$13.6\mathrm{eV}$
    2. B.$1.5\mathrm{eV}$
    3. C.$12.1\mathrm{eV}$
    4. D.$1.9\mathrm{eV}$
    Show answer

    Answer: C

21. Q422024 · 1 Feb 2024 · Shift 1

    The de Broglie wavelengths of a proton and an $\alpha$ particle are $\lambda$ and $2\lambda$ respectively. The ratio of the velocities of proton and $\alpha$ particle will be :

    1. A.$8:1$
    2. B.$1:2$
    3. C.$1:8$
    4. D.$4:1$
    Show answer

    Answer: A

22. Q552024 · 1 Feb 2024 · Shift 1· Numerical answer

    The radius of a nucleus of mass number 64 is 4.8 fermi. Then the mass number of another nucleus having radius of 4 fermi is $\frac{1000}{x}$, where $x$ is ____.

    Show answer

    Answer: 27

23. Q312024 · 1 Feb 2024 · Shift 2

    From the statements given below : (A) The angular momentum of an electron in $n^{\text{th}}$ orbit is an integral multiple of $\hslash$. (B) Nuclear forces do not obey inverse square law. (C) Nuclear forces are spin dependent. (D) Nuclear forces are central and charge independent. (E) Stability of nucleus is inversely proportional to the value of packing fraction. Choose the correct answer from the options given below :

    1. A.(B), (C), (D), (E) only
    2. B.(A), (C), (D), (E) only
    3. C.(A), (B), (C), (E) only
    4. D.(A), (B), (C), (D) only
    Show answer

    Answer: C

24. Q332024 · 1 Feb 2024 · Shift 2

    Monochromatic light of frequency $6\times 10^{14}\text{ Hz}$ is produced by a laser. The power emitted is $2\times 10^{-3}\text{ W}$. How many photons per second on an average, are emitted by the source ? (Given $\mathrm{h}=6.63\times 10^{-34}\text{ Js}$ )

    1. A.$5\times 10^{15}$
    2. B.$7\times 10^{16}$
    3. C.$6\times 10^{15}$
    4. D.$9\times 10^{18}$
    Show answer

    Answer: A

25. Q392024 · 31 Jan 2024 · Shift 1

    When a metal surface is illuminated by light of wavelength $\lambda$, the stopping potential is $8\mathrm{V}$. When the same surface is illuminated by light of wavelength $3\lambda$, stopping potential is $2\mathrm{V}$. The threshold wavelength for this surface is:

    1. A.$3\lambda$
    2. B.$9\lambda$
    3. C.$5\lambda$
    4. D.$4.5\lambda$
    Show answer

    Answer: B