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

2022 28 questions

1. Q472022 · 29 Jul 2022 · Shift 1

   Find the ratio of energies of photons produced due to transition of an electron of hydrogen atom from its (i) second permitted energy level to the first level, and (ii) the highest permitted energy level to the first permitted level.

   1. A.3 : 4
   2. B.4 : 3
   3. C.1 : 4
   4. D.4 : 1
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   Answer: A

2. Q492022 · 29 Jul 2022 · Shift 2

   Read the following statements : (A) Volume of the nucleus is directly proportional to the mass number. (B) Volume of the nucleus is independent of mass number. (C) Density of the nucleus is directly proportional to the mass number. (D) Density of the nucleus is directly proportional to the cube root of the mass number. (E) Density of the nucleus is independent of the mass number. Choose the correct option from the following options.

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

   Answer: B

3. Q602022 · 29 Jul 2022 · Shift 2· Numerical answer

   Two radioactive materials A and B have decay constants $25\lambda$ and $16\lambda$ respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of B to that of A will be "e" after a time $\frac{1}{a\lambda }$. The value of a is ____.

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   Answer: 9

4. Q492022 · 28 Jul 2022 · Shift 1

   The half life period of a radioactive substance is $60\text{ days}$. The time taken for $\frac{7}{8}\text{th}$ of its original mass to disintegrate will be :

   1. A.$120\text{ days}$
   2. B.$130\text{ days}$
   3. C.$180\text{ days}$
   4. D.$20\text{ days}$
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   Answer: C

5. Q582022 · 28 Jul 2022 · Shift 1· Numerical answer

   A freshly prepared radioactive source of half life 2 hours 30 minutes emits radiation which is 64 times the permissible safe level. The minimum time, after which it would be possible to work safely with source, will be _________ hours.

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   Answer: 15

6. Q472022 · 28 Jul 2022 · Shift 2

   Two streams of photons, possessing energies equal to five and ten times the work function of metal are incident on the metal surface successively. The ratio of maximum velocities of the photoelectron emitted, in the two cases respectively, will be

   1. A.1 : 2
   2. B.1 : 3
   3. C.2 : 3
   4. D.3 : 2
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   Answer: C

7. Q482022 · 28 Jul 2022 · Shift 2

   A radioactive sample decays $\frac{7}{8}$ times its original quantity in 15 minutes. The half-life of the sample is

   1. A.$5\text{ min}$
   2. B.$7.5\text{ min}$
   3. C.$15\text{ min}$
   4. D.$30\text{ min}$
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   Answer: A

8. Q492022 · 27 Jul 2022 · Shift 1

   What is the half-life period of a radioactive material if its activity drops to $1/16^{\text{th}}$ of its initial value in 30 years?

   1. A.$9.5\text{ years}$
   2. B.$8.5\text{ years}$
   3. C.$7.5\text{ years}$
   4. D.$10.5\text{ years}$
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   Answer: C

9. Q482022 · 27 Jul 2022 · Shift 2

   The activity of a radioactive material is $6.4\times 10^{-4}\mathrm{curie}$. Its half life is 5 days. The activity will become $5\times 10^{-6}\mathrm{curie}$ after :

   1. A.7 days
   2. B.15 days
   3. C.25 days
   4. D.35 days
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   Answer: D

10. Q322022 · 26 Jul 2022 · Shift 1

    A parallel beam of light of wavelength $900\mathrm{nm}$ and intensity $100\mathrm{W}{\mathrm{m}}^{-2}$ is incident on a surface perpendicular to the beam. The number of photons crossing $1\mathrm{c}{\mathrm{m}}^2$ area perpendicular to the beam in one second is :

    1. A.$3\times 10^{16}$
    2. B.$4.5\times 10^{16}$
    3. C.$4.5\times 10^{17}$
    4. D.$4.5\times 10^{20}$
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    Answer: B

11. Q502022 · 26 Jul 2022 · Shift 1

    The disintegration rate of a certain radioactive sample at any instant is $4250$ disintegrations per minute. $10$ minutes later, the rate becomes $2250$ disintegrations per minute. The approximate decay constant is : (Take ${\log }_{10}1.88=0.274$)

    1. A.$0.02\mathrm{mi}{\mathrm{n}}^{-1}$
    2. B.$2.7\mathrm{mi}{\mathrm{n}}^{-1}$
    3. C.$0.063\mathrm{mi}{\mathrm{n}}^{-1}$
    4. D.$6.3\mathrm{mi}{\mathrm{n}}^{-1}$
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    Answer: C

12. Q582022 · 26 Jul 2022 · Shift 1· Numerical answer

    In the hydrogen spectrum, $\lambda$ be the wavelength of first transition line of Lyman series. The wavelength difference will be "$a\lambda$" between the wavelength of $3^{\mathrm{rd}}$ transition line of Paschen series and that of $2^{\mathrm{nd}}$ transition line of Balmer series where $\mathrm{a}=$ ____.

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    Answer: 5

13. Q472022 · 25 Jul 2022 · Shift 2

    Hydrogen atom from excited state comes to the ground state by emitting a photon of wavelength $\lambda$. The value of principal quantum number '$n$' of the excited state will be : (R : Rydberg constant)

    1. A.$\sqrt{\frac{\lambda R}{\lambda -1}}$
    2. B.$\sqrt{\frac{\lambda R}{\lambda R-1}}$
    3. C.$\sqrt{\frac{\lambda }{\lambda R-1}}$
    4. D.$\sqrt{\frac{\lambda R^2}{\lambda R-1}}$
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    Answer: B

14. Q542022 · 25 Jul 2022 · Shift 2· Numerical answer

    $\frac{x}{x+4}$ is the ratio of energies of photons produced due to transition of an electron of hydrogen atom from its (i) third permitted energy level to the second level and (ii) the highest permitted energy level to the second permitted level. The value of x will be ___________.

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    Answer: 5

15. Q462022 · 30 Jun 2022 · Shift 1

    A source of monochromatic light liberates $9\times 10^{20}$ photon per second with wavelength $600\text{ nm}$ when operated at $400\text{ W}$. The number of photons emitted per second with wavelength of $800\text{ nm}$ by the source of monochromatic light operating at same power will be :

    1. A.$12\times 10^{20}$
    2. B.$6\times 10^{20}$
    3. C.$9\times 10^{20}$
    4. D.$24\times 10^{20}$
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    Answer: A

16. Q572022 · 30 Jun 2022 · Shift 1· Numerical answer

    A hydrogen atom in its first excited state absorbs a photon of energy $x\times 10^{-2}\text{ eV}$ and excited to a higher energy state where the potential energy of electron is $-1.08\text{ eV}$. The value of $x$ is ___________.

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    Answer: 286

17. Q492022 · 28 Jun 2022 · Shift 2

    Following statements related to radioactivity are given below : (A) Radioactivity is a random and spontaneous process and is dependent on physical and chemical conditions. (B) The number of un-decayed nuclei in the radioactive sample decays exponentially with time. (C) Slope of the graph of ${\log }_{\mathrm{e}}$ (no. of undecayed nuclei) Vs. time represents the reciprocal of mean life time ($\tau$). (D) Product of decay constant ($\lambda$) and half-life time (${\mathrm{T}}_{1/2}$) is not constant. Choose the most appropriate answer from the options given below :

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

    Answer: C

18. Q432022 · 27 Jun 2022 · Shift 1

    An $\alpha$ particle and a carbon 12 atom has same kinetic energy K. The ratio of their de-Broglie wavelengths $({\lambda }_{\alpha }:{\lambda }_{C12})$ is :

    1. A.$1:\sqrt{3}$
    2. B.$\sqrt{3}:1$
    3. C.$3:1$
    4. D.$2:\sqrt{3}$
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    Answer: B

19. Q482022 · 27 Jun 2022 · Shift 2

    Given below are two statements : Statement I : In hydrogen atom, the frequency of radiation emitted when an electron jumps from lower energy orbit (${\text{E}}_1$) to higher energy orbit (${\text{E}}_2$), is given as $\text{h}f={\text{E}}_1-{\text{E}}_2$ Statement II : The jumping of electron from higher energy orbit (${\text{E}}_2$) to lower energy orbit (${\text{E}}_1$) is associated with frequency of radiation given as $f=({\text{E}}_2-{\text{E}}_1)/\text{h}$ This condition is Bohr's frequency condition. In the light of the above statements, choose the correct answer from the options given below :

    1. A.Both Statement I and Statement II are true.
    2. B.Both Statement I and Statement II are false.
    3. C.Statement I is correct but Statement II is false.
    4. D.Statement I is incorrect but Statement II is true.
    Show answer

    Answer: D

20. Q462022 · 26 Jun 2022 · Shift 1

    An electron with speed v and a photon with speed c have the same de-Broglie wavelength. If the kinetic energy and momentum of electron are ${\mathrm{E}}_e$ and ${\mathrm{p}}_e$ and that of photon are ${\mathrm{E}}_{ph}$ and ${\mathrm{p}}_{ph}$ respectively. Which of the following is correct?

    1. A.$\frac{{\mathrm{E}}_e}{{\mathrm{E}}_{ph}}=\frac{2c}{v}$
    2. B.$\frac{{\mathrm{E}}_e}{{\mathrm{E}}_{ph}}=\frac{v}{2c}$
    3. C.$\frac{{\mathrm{p}}_e}{{\mathrm{p}}_{ph}}=\frac{2c}{v}$
    4. D.$\frac{{\mathrm{p}}_e}{{\mathrm{p}}_{ph}}=\frac{v}{2c}$
    Show answer

    Answer: B

21. Q492022 · 26 Jun 2022 · Shift 1

    How many alpha and beta particles are emitted when Uranium ${}_{92}{\mathrm{U}}^{238}$ decays to lead ${}_{82}{\mathrm{Pb}}^{206}$ ?

    1. A.3 alpha particles and 5 beta particles
    2. B.6 alpha particles and 4 beta particles
    3. C.4 alpha particles and 5 beta particles
    4. D.8 alpha particles and 6 beta particles
    Show answer

    Answer: D

22. Q482022 · 26 Jun 2022 · Shift 2

    A radioactive nucleus can decay by two different processes. Half-life for the first process is 3.0 hours while it is 4.5 hours for the second process. The effective half-life of the nucleus will be:

    1. A.3.75 hours
    2. B.0.56 hours
    3. C.0.26 hours
    4. D.1.80 hours
    Show answer

    Answer: D

23. Q592022 · 26 Jun 2022 · Shift 2· Numerical answer

    The stopping potential for photoelectrons emitted from a surface illuminated by light of wavelength $6630\text{A˚}$ is 0.42 V. If the threshold frequency is $x\times 10^{13}\text{ /s}$, where x is ________ (nearest integer). (Given, speed light $=3\times 10^8\text{ m/s}$, Planck's constant $=6.63\times 10^{-34}\text{ Js}$)

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    Answer: 35

24. Q452022 · 25 Jun 2022 · Shift 1

    The ratio for the speed of the electron in the $3^{\text{rd}}$ orbit of ${\mathrm{He}}^{+}$ to the speed of the electron in the $3^{\text{rd}}$ orbit of hydrogen atom will be :

    1. A.$1:1$
    2. B.$1:2$
    3. C.$4:1$
    4. D.$2:1$
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    Answer: D

25. Q462022 · 25 Jun 2022 · Shift 2

    A proton, a neutron, an electron and an $\alpha$ particle have same energy. If ${\lambda }_{\mathrm{p}}$, ${\lambda }_{\mathrm{n}}$, ${\lambda }_{\mathrm{e}}$ and ${\lambda }_{\alpha }$ are the de Broglie's wavelengths of proton, neutron, electron and $\alpha$ particle respectively, then choose the correct relation from the following :

    1. A.${\lambda }_{\mathrm{p}}={\lambda }_{\mathrm{n}}>{\lambda }_{\mathrm{e}}>{\lambda }_{\alpha }$
    2. B.${\lambda }_{\alpha }<{\lambda }_{\mathrm{n}}<{\lambda }_{\mathrm{p}}<{\lambda }_{\mathrm{e}}$
    3. C.${\lambda }_{\mathrm{e}}<{\lambda }_{\mathrm{p}}={\lambda }_{\mathrm{n}}>{\lambda }_{\alpha }$
    4. D.${\lambda }_{\mathrm{e}}={\lambda }_{\mathrm{p}}={\lambda }_{\mathrm{n}}={\lambda }_{\alpha }$
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    Answer: B