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

2020 19 questions

1. Q282020 · 6 Sept 2020 · Shift 1

   An electron, a doubly ionized helium ion ($\mathrm{H}{\mathrm{e}}^{++}$) and a proton are having the same kinetic energy. The relation between their respective de-Broglie wavelengths ${\lambda }_e$, ${\lambda }_{\mathrm{H}{\mathrm{e}}^{++}}$ and ${\lambda }_p$ is :

   1. A.${\lambda }_e>{\lambda }_{\mathrm{H}{\mathrm{e}}^{++}}>{\lambda }_p$
   2. B.${\lambda }_e<{\lambda }_p<{\lambda }_{\mathrm{H}{\mathrm{e}}^{++}}$
   3. C.${\lambda }_e>{\lambda }_p>{\lambda }_{\mathrm{H}{\mathrm{e}}^{++}}$
   4. D.${\lambda }_e<{\lambda }_{\mathrm{H}{\mathrm{e}}^{++}}={\lambda }_p$
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   Answer: C

2. Q322020 · 6 Sept 2020 · Shift 1

   You are given that Mass of ${}_3^7\mathrm{Li}=7.0160\text{u}$, Mass of ${}_2^4\mathrm{He}=4.0026\text{u}$ and Mass of ${}_1^1\mathrm{H}=1.0079\text{u}$. When $20\text{ g}$ of ${}_3^7\mathrm{Li}$ is converted into ${}_2^4\mathrm{He}$ by proton capture, the energy liberated, (in $\mathrm{kWh}$), is : $[\text{Mass of nucleon}=1\mathrm{GeV}/c^2]$

   1. A.$6.82\times 10^5$
   2. B.$4.5\times 10^5$
   3. C.$8\times 10^6$
   4. D.$1.33\times 10^6$
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   Answer: D

3. Q382020 · 6 Sept 2020 · Shift 2

   Assuming the nitrogen molecule is moving with r.m.s. velocity at $400\text{ K}$, the de-Broglie wavelength of nitrogen molecule is close to : (Given : nitrogen molecule weight : $4.64\times 10^{-26}\text{ kg}$, Boltzmann constant: $1.38\times 10^{-23}J/K$, Planck constant : $6.63\times 10^{-34}J.s$)

   1. A.$0.44\text{A˚}$
   2. B.$0.34\text{A˚}$
   3. C.$0.20\text{A˚}$
   4. D.$0.24\text{A˚}$
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   Answer: D

4. Q452020 · 3 Sept 2020 · Shift 1

   In a radioactive material, fraction of active material remaining after time t is 9/16. The fraction that was remaining after t/2 is

   1. A.$\frac{3}{4}$
   2. B.$\frac{4}{5}$
   3. C.$\frac{3}{5}$
   4. D.$\frac{7}{8}$
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   Answer: A

5. Q282020 · 3 Sept 2020 · Shift 2

   Two sources of light emit X-rays of wavelength 1 nm and visible light of wavelength 500 nm, respectively. Both the sources emit light of the same power 200 W. The ratio of the number density of photons of X-rays to the number density of photons of the visible light of the given wavelengths is :

   1. A.$\frac{1}{500}$
   2. B.500
   3. C.250
   4. D.$\frac{1}{250}$
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   Answer: A

6. Q452020 · 3 Sept 2020 · Shift 2

   The radius R of a nucleus of mass number A can be estimated by the formula $\mathrm{R}=(1.3\times 10^{-15}){\mathrm{A}}^{1/3}\mathrm{m}$. It follows that the mass density of a nucleus is of the order of : $({\mathrm{M}}_{prot.}\cong {\mathrm{M}}_{\mathrm{neut}}\simeq 1.67\times 10^{-27}\mathrm{kg})$

   1. A.$10^{24}\mathrm{kg}{\mathrm{m}}^{-3}$
   2. B.$10^{10}\mathrm{kg}{\mathrm{m}}^{-3}$
   3. C.$10^{17}\mathrm{kg}{\mathrm{m}}^{-3}$
   4. D.$10^3\mathrm{kg}{\mathrm{m}}^{-3}$
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   Answer: C

7. Q422020 · 2 Sept 2020 · Shift 1

   In a reactor, 2 kg of ${}_{92}{\mathrm{U}}^{235}$ fuel is fully used up in 30 days. The energy released per fission is 200 MeV. Given that the Avogadro number, $\mathrm{N}=6.023\times 10^{26}$ per kilo mole and $1\text{ eV}=1.6\times 10^{-19}\text{ J}$. The power output of the reactor is close to

   1. A.125 MW
   2. B.60 MW
   3. C.54 MW
   4. D.35 MW
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   Answer: B

8. Q482020 · 2 Sept 2020 · Shift 1· Numerical answer

   When radiation of wavelength $\lambda$ is used to illuminate a metallic surface, the stopping potential is $V$. When the same surface is illuminated with radiation of wavelength $3\lambda$, the stopping potential is $\frac{V}{4}$. If the threshold wavelength for the metallic surface is $n\lambda$ then value of $n$ will be ____.

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   Answer: 9

9. Q302020 · 2 Sept 2020 · Shift 2

   In a hydrogen atom the electron makes a transition from $(n+1{)}^{\mathrm{th}}$ level to the $n^{\mathrm{th}}$ level. If $n\gg 1$, the frequency of radiation emitted is proportional to :

   1. A.$\frac{1}{n}$
   2. B.$\frac{1}{n^2}$
   3. C.$\frac{1}{n^3}$
   4. D.$\frac{1}{n^4}$
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   Answer: C

10. Q372020 · 2 Sept 2020 · Shift 2

    A particle is moving 5 times as fast as an electron. The ratio of the de-Broglie wavelength of the particle to that of the electron is $1.878\times 10^{-4}$. The mass of the particle is close to

    1. A.$1.2\times 10^{-28}\mathrm{kg}$
    2. B.$9.1\times 10^{-31}\mathrm{kg}$
    3. C.$4.8\times 10^{-27}\mathrm{kg}$
    4. D.$9.7\times 10^{-28}\mathrm{kg}$
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    Answer: D

11. Q332020 · 9 Jan 2020 · Shift 1

    A particle moving with kinetic energy E has de Broglie wavelength $\lambda$. If energy $\Delta \mathrm{E}$ is added to its energy, the wavelength become $\lambda /2$. Value of $\Delta \mathrm{E}$, is :

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

12. Q392020 · 9 Jan 2020 · Shift 2

    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 ?

    1. A.35.8 nm
    2. B.11.4 nm
    3. C.8.6 nm
    4. D.24.2 nm
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    Answer: B

13. Q272020 · 8 Jan 2020 · Shift 1

    When photon of energy 4.0 eV strikes the surface of a metal A, the ejected photoelectrons have maximum kinetic energy ${\mathrm{T}}_{\mathrm{A}}$ eV and de-Broglie wavelength ${\lambda }_A$. The maximum kinetic energy of photoelectrons liberated from another metal B by photon of energy 4.50 eV is ${\mathrm{T}}_{\mathrm{B}}=({\mathrm{T}}_{\mathrm{A}}-1.5)\text{ eV}$. If the de-Broglie wavelength of these photoelectrons ${\lambda }_B=2{\lambda }_A$, then the work function of metal B is :

    1. A.1.5eV
    2. B.4eV
    3. C.2eV
    4. D.3eV
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    Answer: B

14. Q482020 · 8 Jan 2020 · Shift 2· Numerical answer

    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:

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    Answer: 486

15. Q342020 · 7 Jan 2020 · Shift 1

    The time period of revolution of electron in its ground state orbit in a hydrogen atom is $1.6\times 10^{-16}\text{ s}$. The frequency of revolution of the electron in its first excited state (in ${\text{s}}^{-1}$) is :

    1. A.$5.6\times 10^{12}$
    2. B.$1.6\times 10^{14}$
    3. C.$7.8\times 10^{14}$
    4. D.$6.2\times 10^{15}$
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    Answer: C

16. Q482020 · 7 Jan 2020 · Shift 1· Numerical answer

    A beam of electromagnetic radiation of intensity $6.4\times 10^{-5}W/c{\mathrm{m}}^2$ is comprised of wavelength, $\lambda =310\mathrm{nm}$. It falls normally on a metal (work function $\varphi =2\mathrm{eV}$) of surface area of $1\mathrm{c}{\mathrm{m}}^2$. If one in $10^3$ photons ejects an electron, total number of electrons ejected in $1\mathrm{s}$ is $10^{\mathrm{x}}$. ($\mathrm{hc}=1240\mathrm{eVnm}$, $1\mathrm{eV}=1.6\times 10^{-19}\mathrm{J}$), then x is ____.

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    Answer: 11

17. Q262020 · 7 Jan 2020 · Shift 2

    An electron (of mass m) and a photon have the same energy E in the range of a few eV. The ratio of the de-Broglie wavelength associated with the electron and the wavelength of the photon is (c = speed of light in vaccum)

    1. A.$\frac{1}{c}{\left(\frac{2E}{m}\right)}^{\frac{1}{2}}$
    2. B.$\frac{1}{c}{\left(\frac{E}{2m}\right)}^{\frac{1}{2}}$
    3. C.${\left(\frac{E}{2m}\right)}^{\frac{1}{2}}$
    4. D.$c(2mE{)}^{\frac{1}{2}}$
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    Answer: B

18. Q422020 · 7 Jan 2020 · Shift 2

    The activity of a radioactive sample falls from $700{\text{ s}}^{-1}$ to $500{\text{ s}}^{-1}$ in 30 minutes. Its half life is close to:

    1. A.62 min
    2. B.66 min
    3. C.72 min
    4. D.52 min
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    Answer: A

19. Q492020 · 7 Jan 2020 · Shift 2· Numerical answer

    M grams of steam at $100^{\circ }\mathrm{C}$ is mixed with 200 g of ice at its melting point in a thermally insulated container. If it produced liquid water at $40^{\circ }\mathrm{C}$ [heat of vaporization of water is $540\text{ cal/g}$ and heat of fusion of ice is $80\text{ cal/g}$] the value of M is ___

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    Answer: 40