JEE Physics Atoms MCQs Set 15

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Chapter-wise Objective Questions: Atoms

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Multiple Choice Questions

Question 1: Period of revolution of electron in the nth Bohr's orbit is given by
(a) \( T=\frac{4\epsilon_0^2n^3h^3}{me^4} \)
(b) \( T=4\epsilon_0^2 n^3h^3 \)
(c) \( T=me^4n \)
(d) \( T=2\pi \)
Show Answer & Explanation

Answer: (a) \( T=\frac{4\epsilon_0^2n^3h^3}{me^4} \)

Explanation:
1. T = 2πr/v = 4ε₀²n³h³/(me⁴).

Teacher's Note:
1. Recall the basic fact.

Question 2: The significant result deduced from the Rutherford's scattering experiment is that
(a) whole of the positive charge is concentrated at the centre of atom
(b) there are neutrons inside the nucleus
(c) α-particles are helium nuclei
(d) electrons are embedded in the atom
Show Answer & Explanation

Answer: (a) whole of the positive charge is concentrated at the centre of atom

Explanation:
1. Large-angle scattering showed that all the positive charge is concentrated in the nucleus.

Teacher's Note:
1. Recall the basic fact.

Question 3: Kα wavelength emitted by an atom of atomic number Z = 11 is λ. Find the atomic number for an atom that emits Kα radiation with wavelength 4λ.
(a) Z = 6
(b) Z = 4
(c) Z = 11
(d) Z = 44
Show Answer & Explanation

Answer: (a) Z = 6

Explanation:
1. Moseley: 1/λ ∝ (Z − 1)².
2. (Z' − 1)² = (Z − 1)²/4, so Z' − 1 = 5 and Z' = 6.

Teacher's Note:
1. Recall the basic fact.

Question 4: The Rutherford α-particle experiment shows that most of the α-particles pass through almost unscattered while some are scattered through large angles. What information does it give about the structure of the atom?
(a) Atom is hollow.
(b) The whole mass of the atom is concentrated in a small centre called nucleus
(c) Nucleus is positively charged
(d) All of the above
Show Answer & Explanation

Answer: (d) All of the above

Explanation:
1. Most of the atom is empty space, and the mass and positive charge are concentrated in a tiny nucleus.

Teacher's Note:
1. Recall the basic fact.

Question 5: According to Bohr, the difference between the energies of the electron in the two orbits is equal to
(a) \( h\nu \)
(b) \( hc/\lambda \)
(c) \( \text{both (a) and (b)} \)
(d) \( \text{neither (a) nor (b)} \)
Show Answer & Explanation

Answer: (c) \( \text{both (a) and (b)} \)

Explanation:
1. ΔE = hν = hc/λ.

Teacher's Note:
1. Recall the basic fact.

Question 6: The angular speed of the electron in the nth orbit of Bohr hydrogen atom is
(a) directly proportional to n
(b) inversely proportional to √n
(c) inversely proportional to n²
(d) inversely proportional to n³
Show Answer & Explanation

Answer: (d) inversely proportional to n³

Explanation:
1. ω = v/r ∝ (1/n)/n² = 1/n³.

Teacher's Note:
1. Recall the basic fact.

Question 7: Match the transitions in Column I with the series in Column II.
Column IColumn II
(A) n = 5 to n = 2(1) Lyman series
(B) n = 8 to n = 4(2) Brackett series
(C) n = 3 to n = 1(3) Paschen series
(D) n = 4 to n = 3(4) Balmer series

(a) A-4, B-2, C-1, D-3
(b) A-2, B-4, C-1, D-3
(c) A-4, B-2, C-3, D-1
(d) A-4, B-3, C-1, D-2
Show Answer & Explanation

Answer: (a) A-4, B-2, C-1, D-3

Explanation:
1. Final level 1 is Lyman, 2 Balmer, 3 Paschen and 4 Brackett.
2. 5→2 Balmer, 8→4 Brackett, 3→1 Lyman, 4→3 Paschen.

Teacher's Note:
1. The series depends on the lower level.

Question 8: Rutherford's α-particle scattering experiment concludes that I. there is a heavy mass at centre II. electrons are revolving around the nucleus
(a) I only
(b) II only
(c) I and II
(d) None of these
Show Answer & Explanation

Answer: (a) I only

Explanation:
1. The experiment shows a heavy central nucleus; the motion of electrons was not shown by it.

Teacher's Note:
1. Recall the basic fact.

Question 9: Electron in hydrogen atom first jumps from third excited state to second excited state and then from second excited to the first excited state. The ratio of the wavelengths λ₁ : λ₂ emitted in the two cases is
(a) 7/5
(b) 27/20
(c) 27/5
(d) 20/7
Show Answer & Explanation

Answer: (d) 20/7

Explanation:
1. 4 → 3: 1/λ₁ = R(1/9 − 1/16) = 7R/144.
2. 3 → 2: 1/λ₂ = R(1/4 − 1/9) = 5R/36 = 20R/144.
3. λ₁/λ₂ = 20/7.

Teacher's Note:
1. Recall the basic fact.

Question 10: In a hydrogen atom, which of the following electronic transitions would involve the maximum energy change?
(a) n = 2 to n = 1
(b) n = 3 to n = 1
(c) n = 4 to n = 2
(d) n = 3 to n = 2
Show Answer & Explanation

Answer: (b) n = 3 to n = 1

Explanation:
1. Energy changes: 10.2, 12.1, 2.55 and 1.89 eV. The largest is 3 → 1.

Teacher's Note:
1. Recall the basic fact.

Question 11: If r is the radius of the lowest orbit of Bohr's model of H-atom, then the radius of nth orbit is
(a) \( rn^2 \)
(b) \( 2r \)
(c) \( \frac{n^2}{r} \)
(d) \( rn \)
Show Answer & Explanation

Answer: (a) \( rn^2 \)

Explanation:
1. rₙ = n²r.

Teacher's Note:
1. Recall the basic fact.

Question 12: When an atomic gas or vapour is excited at low pressure, by passing an electric current through it then
(a) emission spectrum is observed
(b) absorption spectrum is observed
(c) band spectrum is observed
(d) both (b) and (c)
Show Answer & Explanation

Answer: (a) emission spectrum is observed

Explanation:
1. An excited atomic gas emits light, giving a line emission spectrum.

Teacher's Note:
1. Recall the basic fact.

Question 13: Match Column I with Column II.
Column IColumn II
(A) J.J. Thomson(1) Nuclear model of the atom
(B) E. Rutherford(2) Plum pudding model of the atom
(C) Franck-Hertz(3) Explanation of the hydrogen spectrum
(D) Niels Bohr(4) Existence of discrete energy levels in atoms

(a) A-3, B-1, C-4, D-2
(b) A-2, B-1, C-4, D-3
(c) A-2, B-4, C-1, D-3
(d) A-1, B-2, C-4, D-3
Show Answer & Explanation

Answer: (b) A-2, B-1, C-4, D-3

Explanation:
1. Thomson proposed the plum pudding model.
2. Rutherford proposed the nuclear model.
3. Franck-Hertz showed discrete energy levels.
4. Bohr explained the hydrogen spectrum.

Teacher's Note:
1. Match each scientist with the contribution.

Question 14: If the angular momentum of an electron in an orbit is J then the K.E. of the electron in that orbit is
(a) \( \frac{J^2}{2mr^2} \)
(b) \( \frac{Jv}{r} \)
(c) \( \frac{J^2}{2m} \)
(d) \( \frac{J^2}{2\pi} \)
Show Answer & Explanation

Answer: (a) \( \frac{J^2}{2mr^2} \)

Explanation:
1. J = mvr, so v = J/mr and KE = ½mv² = J²/(2mr²).

Teacher's Note:
1. Recall the basic fact.

Question 15: The energy of an excited state of H atom is −0.85 eV. What will be the quantum number of the orbit, if the ground state energy for hydrogen is −13.6 eV?
(a) 4
(b) 3
(c) 2
(d) 1
Show Answer & Explanation

Answer: (a) 4

Explanation:
1. n² = 13.6/0.85 = 16, so n = 4.

Teacher's Note:
1. Recall the basic fact.

Question 16: Hydrogen atom is excited from ground state to another state with principal quantum number equal to 4. Then the number of spectral lines in the emission spectra will be
(a) 2
(b) 3
(c) 5
(d) 6
Show Answer & Explanation

Answer: (d) 6

Explanation:
1. N = 4 × 3/2 = 6.

Teacher's Note:
1. Recall the basic fact.

Question 17:
Assertion (A): Between any two given energy levels, the number of absorption transitions is always less than the number of emission transitions.
Reason (R): Absorption transitions start from the lowest energy level only and may end at any higher energy level. But emission transitions may start from any higher energy level and end at any energy level below it.
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is not the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
Show Answer & Explanation

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. Absorption occurs only from the lowest level (in normal conditions), whereas emission can start from any higher level.
2. So emission lines are more numerous, as the second statement explains.

Teacher's Note:
1. Count how many starting levels each process allows.

Question 18:
Assertion (A): The force of repulsion between atomic nucleus and α-particle varies with distance according to inverse square law.
Reason (R): Rutherford did α-particle scattering experiment.
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is not the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
Show Answer & Explanation

Answer: (b) Both A and R are true, but R is not the correct explanation of A.

Explanation:
1. The Coulomb force follows the inverse square law, and Rutherford did the experiment, but the reason does not explain the assertion.

Teacher's Note:
1. Both are true but unrelated as cause and effect.

Question 19: According to Planck's quantum theory any electromagnetic radiation is
(a) continuously emitted
(b) continuously absorbed
(c) emitted or absorbed in discrete units
(d) None of these
Show Answer & Explanation

Answer: (c) emitted or absorbed in discrete units

Explanation:
1. Energy is exchanged in quanta of hν.

Teacher's Note:
1. Recall the basic fact.

Question 20: If R is the Rydberg constant, the energy of an electron in the ground state H atom is
(a) \( \frac{Rc}{h} \)
(b) \( \frac{-1}{Rhc} \)
(c) \( -Rhc \)
(d) \( \frac{vc}{R} \)
Show Answer & Explanation

Answer: (c) \( -Rhc \)

Explanation:
1. E₁ = −13.6 eV = −Rhc.

Teacher's Note:
1. Recall the basic fact.

Question 21:
Assertion (A): According to classical theory the proposed path of an electron in Rutherford atom model will be parabolic.
Reason (R): According to electromagnetic theory an accelerated particle continuously emits radiation.
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is not the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
Show Answer & Explanation

Answer: (d) A is false, but R is true.

Explanation:
1. Radiating electrons lose energy and spiral inwards, not along a parabola, so the assertion is false.
2. The reason is true.

Teacher's Note:
1. The classical path is a spiral.

Question 22: Electrons in the atom are held to the nucleus by
(a) Coulomb's force
(b) nuclear force
(c) van der Waals force
(d) gravitational force
Show Answer & Explanation

Answer: (a) Coulomb's force

Explanation:
1. The electrostatic (Coulomb) attraction holds the electrons.

Teacher's Note:
1. Recall the basic fact.

Question 23: Ionization energy of a hydrogen-like ion A is greater than that of another hydrogen-like ion B. Let r, u, E and L represent the radius of the orbit, speed of the electron, energy of the atom and orbital angular momentum of the electron respectively in ground state. Then
(a) rA > rB
(b) uA > uB
(c) EA > EB
(d) LA > LB
Show Answer & Explanation

Answer: (b) uA > uB

Explanation:
1. Larger ionisation energy means larger Z.
2. r ∝ 1/Z gives rA < rB.
3. u ∝ Z gives uA > uB.
4. The energy is more negative for A, so EA < EB, and L is the same.

Teacher's Note:
1. Recall the basic fact.

Question 24: The energy of a hydrogen atom in the ground state is −13.6 eV. The energy of a He⁺ ion in the first excited state will be
(a) −13.6 eV
(b) −27.2 eV
(c) −54.4 eV
(d) −6.8 eV
Show Answer & Explanation

Answer: (a) −13.6 eV

Explanation:
1. E = −13.6 Z²/n² = −13.6 × 4/4 = −13.6 eV.

Teacher's Note:
1. Recall the basic fact.

Question 25: According to classical theory, Rutherford's atomic model is
(a) stable
(b) unstable
(c) meta stable
(d) both (a) and (b)
Show Answer & Explanation

Answer: (b) unstable

Explanation:
1. The orbiting electron radiates and spirals into the nucleus, so the atom would be unstable.

Teacher's Note:
1. Recall the basic fact.

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