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

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : The binding energy per nucleon is found to be practically independent of the atomic number A , for nuclei with mass numbers between 30 and 170 . Reason (R) : Nuclear force is long range. In the light of the above statements, choose the correct answer from the options given below :

1. A.(A) is true but (R) is false
2. B.Both (A) and (R) are true and (R) is the correct explanation of (A)
3. C.(A) is false but (R) is true
4. D.Both (A) and (R) are true but (R) is NOT the correct explanation of (A)

In photoelectric effect an em-wave is incident on a metal surface and electrons are ejected from the surface. If the work function of the metal is $2.14\text{ eV}$ and stopping potential is $2\text{ V}$ , what is the wavelength of the em-wave? (Given $hc=1242\mathrm{eVnm}$ where $\mathrm{h}$ is the Planck's constant and $\mathrm{c}$ is the speed of light in vacuum.)

1. A.$400\text{ nm}$
2. B.$600\text{ nm}$
3. C.$300\text{ nm}$
4. D.$200\text{ nm}$

The work functions of cesium (Cs) and lithium (Li) metals are 1.9 eV and 2.5 eV , respectively. If we incident a light of wavelength 550 nm on these two metal surfaces, then photo-electric effect is possible for the case of

1. A.Both Cs and Li
2. B.Neither Cs nor Li
3. C.Li only
4. D.Cs only

An electron in the ground state of the hydrogen atom has the orbital radius of $5.3\times 10^{-11}\text{ m}$ while that for the electron in third excited state is $8.48\times 10^{-10}\text{ m}$. The ratio of the de Broglie wavelengths of electron in the excited state to that in the ground state is

1. A.4
2. B.3
3. C.9
4. D.16

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.${\lambda }_{\mathrm{p}}<{\lambda }_{\mathrm{e}}<{\lambda }_{\alpha }$

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.

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

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

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.$1:\frac{1}{\sqrt{1836}}$

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.$0.2\mu \text{g}$

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 $=6.72\times 10^{-27}\text{ kg}$)

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.$(M_0-12M_n)C^2$

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.${\mathrm{K}}_{\mathrm{p}}={{\mathrm{K}}_{\mathrm{e}}}^2$

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

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.$1.5\mathrm{V}$

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 $hc=1245\text{ eV nm},e=1.6\times 10^{-19}\text{ C}$).

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.

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 ____ $\mathring{\mathrm{A}}$.

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.${}_{56}^{144}\mathrm{Ba}+{}_{36}^{89}\mathrm{Kr}+3{}_0^1\mathrm{n}$

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

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 $=1.6\times 10^{-27}\mathrm{kg}$]

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.$8\frac{h}{\pi }$

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 $c^2=931\text{ MeV}/u$.

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.$1.9\mathrm{eV}$

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.$4:1$