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

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2025 24 questions

Q302025 · 8 Apr 2025 · Shift 2
For a nucleus of mass number $A$ and radius $R$ , the mass density of nucleus can be represented as
1. A. $A^{\frac{2}{3}}$
2. B.Independent of $A$
3. C. $A^{3}$
4. D. $A^{\frac{1}{3}}$
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Answer: B
Q492025 · 8 Apr 2025 · Shift 2· Numerical answer
An electron is released from rest near an infinite non-conducting sheet of uniform charge density ' $- σ$ '. The rate of change of de-Broglie wave length associated with the electron varies inversely as $n^{th}$ power of time. The numerical value of $n$ is .
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Answer: 2
Q352025 · 4 Apr 2025 · Shift 1
Considering the Bohr model of hydrogen like atoms, the ratio of the radius of $5^{th}$ orbit of the electron in $L i^{2 +}$ and $H e^{+}$ is
1. A. $\frac{3}{2}$
2. B. $\frac{2}{3}$
3. C. $\frac{4}{9}$
4. D. $\frac{9}{4}$
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Answer: B
Q442025 · 4 Apr 2025 · Shift 1
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A : In photoelectric effect, on increasing the intensity of incident light the stopping potential increases. Reason R : Increase in intensity of light increases the rate of photoelectrons emitted, provided the frequency of incident light is greater than threshold frequency. In the light of the above statements, choose the correct answer from the options given below
1. A.Both A and R are true and R is the correct explanation of A
2. B.A is false but R is true
3. C.Both A and R are true but R is NOT the correct explanation of A
4. D.A is true but R is false
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Answer: B
Q272025 · 4 Apr 2025 · Shift 2
1. A.
2. B.
3. C.
4. D.
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Answer: B
Q452025 · 4 Apr 2025 · Shift 2
Given below are two statements : Statement (I) : The dimensions of Planck's constant and angular momentum are same. Statement (II) : In Bohr's model electron revolve around the nucleus only in those orbits for which angular momentum is integral multiple of Planck's constant. In the light of the above statements, choose the most appropriate answer from the options given below :
1. A.Both Statement I and Statement II are correct
2. B.Statement I is correct but Statement II is incorrect
3. C.Both Statement I and Statement II are incorrect
4. D.Statement I is incorrect but Statement II is correct
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Answer: B
Q302025 · 3 Apr 2025 · Shift 1
The work function of a metal is 3 eV . The color of the visible light that is required to cause emission of photoelectrons is
1. A.Red
2. B.Green
3. C.Blue
4. D.Yellow
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Answer: C
Q382025 · 3 Apr 2025 · Shift 1
Match the LIST-I with LIST-II $List - I A. B. C. D._{0}^{1} n +_{92}^{235} U \to_{54}^{140} Xe +_{38}^{94} Sr + 2_{0}^{1} n 2 H_{2} + O_{2} \to 2 H_{2} O_{1}^{2} H +_{1}^{2} H \to_{2}^{3} He +_{0}^{1} n_{1}^{1} H +_{1}^{3} H \to_{1}^{2} H +_{1}^{2} H List - II I. II. III. IV. Chemical reaction Fusion with +ve Q value Fission Fusion with -ve Q value$ Choose the correct answer from the options given below:
1. A.A-II, B-I, C-III, D-IV
2. B.A-III, B-I, C-II, D-IV
3. C.A-III, B-I, C-IV, D-II
4. D.A-II, B-I, C-IV, D-III
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Answer: B
Q432025 · 3 Apr 2025 · Shift 2
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A : The Bohr model is applicable to hydrogen and hydrogen-like atoms only. Reason R : The formulation of Bohr model does not include repulsive force between electrons. 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
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Answer: B
Q462025 · 3 Apr 2025 · Shift 2· Numerical answer
An electron in the hydrogen atom initially in the fourth excited state makes a transition to $n^{th}$ energy state by emitting a photon of energy $2.86 eV$ . The integer value of $n$ will be__________.
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Answer: 2
Q382025 · 2 Apr 2025 · Shift 1
Considering Bohr's atomic model for hydrogen atom : (A) the energy of H atom in ground state is same as energy of $He^{+}$ ion in its first excited state. (B) the energy of H atom in ground state is same as that for $Li^{++}$ ion in its second excited state. (C) the energy of H atom in its ground state is same as that of $He^{+}$ ion for its ground state. (D) the energy of $He^{+}$ ion in its first excited state is same as that for $Li^{++}$ ion in its ground state. Choose the correct answer from the options given below :
1. A.(A), (B) only
2. B.(A), (D) only
3. C.(A), (C) only
4. D.(B), (D) only
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Answer: A
Q392025 · 2 Apr 2025 · Shift 2
Energy released when two deuterons ( $_{1} H^{2}$ ) fuse to form a helium nucleus ( $_{2} He^{4}$ ) is : (Given : Binding energy per nucleon of $_{1} H^{2} = 1.1 MeV$ and binding energy per nucleon of $_{2} He^{4} = 7.0 MeV$ )
1. A. $26.8 MeV$
2. B. $8.1 MeV$
3. C. $23.6 MeV$
4. D. $5.9 MeV$
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Answer: C
Q452025 · 2 Apr 2025 · Shift 2
Assuming the validity of Bohr's atomic model for hydrogen like ions the radius of $L i^{++}$ ion in its ground state is given by $\frac{1}{X} a_{0}$ , where $X =$ ____ (Where $a_{0}$ is the first Bohr's radius.)
1. A.2
2. B.9
3. C.1
4. D.3
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Answer: D
Q272025 · 29 Jan 2025 · Shift 2
In an experiment with photoelectric effect, the stopping potential,
1. A.is $(\frac{1}{e})$ times the maximum kinetic energy of the emitted photoelectrons
2. B.increases with increase in the intensity of the incident light
3. C.decreases with increase in the intensity of the incident light
4. D.increases with increase in the wavelength of the incident light
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Answer: A
Q282025 · 29 Jan 2025 · Shift 2
The number of spectral lines emitted by atomic hydrogen that is in the 4th energy level, is
1. A.3
2. B.6
3. C.1
4. D.0
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Answer: B
Q332025 · 28 Jan 2025 · Shift 1
A proton of mass ' $m_{P}$ ' has same energy ' $E$ ' as that of a photon of wavelength ' $λ$ '. If the proton is moving at non-relativistic speed, then ratio of its de Broglie wavelength to the wavelength of photon is.
1. A. $\frac{1}{c} \frac{E}{m _{p}}$
2. B. $\frac{1}{c} \frac{2 E}{m _{p}}$
3. C. $\frac{1}{2 c} \frac{E}{m _{p}}$
4. D. $\frac{1}{c} \frac{E}{2 m _{p}}$
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Answer: D
Q442025 · 28 Jan 2025 · Shift 1
Choose the correct nuclear process from the below options [ $p$ : proton, $n$ : neutron, $e^{-}$ : electron, $e^{+}$ : positron, $v$ : neutrino, $\overset{v}{ˉ}$ : antineutrino]
1. A. $n \to p + e^{+} + v$
2. B. $n \to p + e^{-} + \overset{v}{ˉ}$
3. C. $n \to p + e^{+} + \overset{v}{ˉ}$
4. D. $n \to p + e^{-} + v$
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Answer: B
Q302025 · 24 Jan 2025 · Shift 1
During the transition of electron from state A to state C of a Bohr atom, the wavelength of emitted radiation is $2000 \overset{˚}{A}$ and it becomes $6000 \overset{˚}{A}$ when the electron jumps from state B to state C. Then the wavelength of the radiation emitted during the transition of electrons from state A to state B is
1. A. $4000 \overset{˚}{A}$
2. B. $6000 \overset{˚}{A}$
3. C. $2000 \overset{˚}{A}$
4. D. $3000 \overset{˚}{A}$
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Answer: D
Q322025 · 24 Jan 2025 · Shift 2
In photoelectric effect, the stopping potential ( $V_{0}$ ) v/s frequency ( $ν$ ) curve is plotted. ( h is the Planck's constant and $ϕ_{0}$ is work function of metal ) (A) $V_{0} v/s ν$ is linear. (B) The slope of $V_{0} v/s ν$ curve $= \frac{ϕ _{0}}{h}$ (C) h constant is related to the slope of $V_{0} v/s ν$ line. (D) The value of electric charge of electron is not required to determine h using the $V_{0} v/s ν$ curve. (E) The work function can be estimated without knowing the value of $h$ . Choose the correct answer from the options given below :
1. A.(A), (C) and (E) only
2. B.(C) and (D) only
3. C.(A), (B) and (C) only
4. D.(D) and (E) only
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Answer: A
Q462025 · 24 Jan 2025 · Shift 2· Numerical answer
The ratio of the power of a light source $S_{1}$ to that of the light source $S_{2}$ is 2. $S_{1}$ is emitting $2 \times 1 0^{15}$ photons per second at 600 nm . If the wavelength of the source $S_{2}$ is 300 nm , then the number of photons per second emitted by $S_{2}$ is ________ $\times 1 0^{14}$ .
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Answer: 5
Q322025 · 23 Jan 2025 · Shift 2
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)
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Answer: A
Q342025 · 23 Jan 2025 · Shift 2
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 $2.14 eV$ and stopping potential is $2 V$ , what is the wavelength of the em-wave? (Given $h c = 1242 eVnm$ where $h$ is the Planck's constant and $c$ is the speed of light in vacuum.)
1. A. $400 nm$
2. B. $600 nm$
3. C. $300 nm$
4. D. $200 nm$
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Answer: C
Q332025 · 22 Jan 2025 · Shift 1
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
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Answer: D
Q382025 · 22 Jan 2025 · Shift 1
An electron in the ground state of the hydrogen atom has the orbital radius of $5.3 \times 1 0^{- 11} m$ while that for the electron in third excited state is $8.48 \times 1 0^{- 10} m$ . 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
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Answer: A