JEE Physics Atoms MCQs Set 16

Multiple Choice Questions (MCQs) for JEE Physics: Atoms

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Multiple Choice Questions

Question 1: Excitation energy of a hydrogen like ion in its excitation state is 40.8 eV. Energy needed to remove the electron from the ion in ground state is
(a) 54.4 eV
(b) 13.6 eV
(c) 40.8 eV
(d) 27.2 eV
Show Answer & Explanation

Answer: (a) 54.4 eV

Explanation:
1. Excitation (1 → 2) energy = 10.2Z² = 40.8, so Z = 2.
2. Ionisation energy = 13.6 × 4 = 54.4 eV.

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

Question 2: If the radius of a hydrogen atom in its ground state is 5.3 × 10⁻¹¹ m, after collision with an electron it is found to have a radius of 21.2 × 10⁻¹¹ m. The principal quantum number of the final orbit is
(a) n = 4
(b) n = 3
(c) n = 2
(d) n = 16
Show Answer & Explanation

Answer: (c) n = 2

Explanation:
1. r ∝ n².
2. n² = 21.2/5.3 = 4, so n = 2.

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

Question 3: The energy of electron in the nth orbit of hydrogen atom is expressed as En = −13.6/n² eV. The shortest and longest wavelength of Lyman series will be
(a) 910 Å, 1213 Å
(b) 5463 Å, 7858 Å
(c) 1315 Å, 1530 Å
(d) None of these
Show Answer & Explanation

Answer: (a) 910 Å, 1213 Å

Explanation:
1. Shortest: 12375/13.6 ≈ 910 Å.
2. Longest: 12375/10.2 ≈ 1213 Å.

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

Question 4: In terms of Bohr radius r₀, the radius of the second Bohr orbit of a hydrogen atom is given by
(a) \( 4r_0 \)
(b) \( 8r_0 \)
(c) \( \sqrt2 r_0 \)
(d) \( 2r_0 \)
Show Answer & Explanation

Answer: (a) \( 4r_0 \)

Explanation:
1. rₙ = n²r₀, so r₂ = 4r₀.

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

Question 5: When an electron jumps from the fourth orbit to the second orbit, one gets the
(a) second line of Paschen series
(b) second line of Balmer series
(c) first line of Pfund series
(d) second line of Lyman series
Show Answer & Explanation

Answer: (b) second line of Balmer series

Explanation:
1. Transitions to n = 2 form the Balmer series. 3 → 2 is the first line and 4 → 2 the second.

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

Question 6: The electrons of Rutherford's model would be expected to lose energy because they
(a) move randomly
(b) jump on nucleus
(c) radiate electromagnetic waves
(d) escape from the atom
Show Answer & Explanation

Answer: (c) radiate electromagnetic waves

Explanation:
1. Orbiting electrons are accelerated and so radiate electromagnetic waves.

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

Question 7: The speed of an electron in the orbit of a H-atom, in the ground state is
(a) \( c \)
(b) \( \frac{c}{2} \)
(c) \( \frac{c}{10} \)
(d) \( \frac{c}{137} \)
Show Answer & Explanation

Answer: (d) \( \frac{c}{137} \)

Explanation:
1. v = αc = c/137 in the first orbit.

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

Question 8: Rutherford's atomic model was unstable because
(a) nuclei will break down
(b) electrons do not remain in orbit
(c) orbiting electrons radiate energy
(d) electrons are repelled by the nucleus
Show Answer & Explanation

Answer: (c) orbiting electrons radiate energy

Explanation:
1. An accelerating charge radiates energy, so the electron would lose energy and collapse.

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

Question 9: If the Kα radiation of Mo (Z = 42) has a wavelength of 0.71 Å. Calculate the wavelength of the corresponding radiation of Cu (Z = 29).
(a) 1.52 Å
(b) 2.52 Å
(c) 0.52 Å
(d) 4.52 Å
Show Answer & Explanation

Answer: (a) 1.52 Å

Explanation:
1. λ ∝ 1/(Z − 1)².
2. λ = 0.71 × (41/28)² = 0.71 × 2.144 = 1.52 Å.

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

Question 10: Four lowest energy levels of H-atom (n = 1 to n = 4) are considered. The number of possible emission lines would be
(a) 3
(b) 4
(c) 5
(d) 6
Show Answer & Explanation

Answer: (d) 6

Explanation:
1. N = n(n − 1)/2 = 4 × 3/2 = 6.

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

Question 11: The ratio of radii of the first three Bohr orbits is
(a) 1 : 1/2 : 1/3
(b) 1 : 2 : 3
(c) 1 : 4 : 9
(d) 1 : 8 : 27
Show Answer & Explanation

Answer: (c) 1 : 4 : 9

Explanation:
1. r ∝ n², so the ratio is 1 : 4 : 9.

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

Question 12: In a hydrogen atom following the Bohr's postulates the product of linear momentum and angular momentum is proportional to (n)ˣ where n is the orbit number. Then x is
(a) 0
(b) 2
(c) −2
(d) 1
Show Answer & Explanation

Answer: (a) 0

Explanation:
1. p = mv ∝ 1/n and L ∝ n.
2. The product is independent of n, so x = 0.

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

Question 13: In Bohr's model electrons are revolving in a circular orbits around the nucleus called as
(a) stationary orbits
(b) non radiating orbits
(c) Bohr's orbits
(d) all of these
Show Answer & Explanation

Answer: (d) all of these

Explanation:
1. These orbits are called stationary, non-radiating or Bohr orbits.

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

Question 14: In Balmer series of emission spectrum of hydrogen, first four lines with different wavelength Hα, Hβ, Hγ and Hδ are obtained. Which line has maximum frequency out of these?
(a) Hα
(b) Hβ
(c) Hγ
(d) Hδ
Show Answer & Explanation

Answer: (d) Hδ

Explanation:
1. Hδ (6 → 2) has the smallest wavelength, hence the highest frequency.

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

Question 15: The linear speed of an electron in Bohr's orbit is
(a) \( \frac{e^2}{2\epsilon_0 nh} \)
(b) \( \frac{e^2}{h} \)
(c) \( \frac{2\epsilon_0 nh}{e^2} \)
(d) \( 2\epsilon_0 h \)
Show Answer & Explanation

Answer: (a) \( \frac{e^2}{2\epsilon_0 nh} \)

Explanation:
1. v = e²/(2ε₀nh).

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

Question 16: The angular momentum of electrons in an atom produces
(a) magnetic moment
(b) Zeeman effect
(c) light
(d) nuclear fission
Show Answer & Explanation

Answer: (a) magnetic moment

Explanation:
1. A revolving charge with angular momentum has a magnetic moment.

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

Question 17: According to Bohr's theory, the wave number of last line of Balmer series is (Given R = 1.1 × 10⁷ m⁻¹)
(a) 5.5 × 10⁵ m⁻¹
(b) 4.4 × 10⁷ m⁻¹
(c) 2.75 × 10⁶ m⁻¹
(d) 2.75 × 10⁸ m⁻¹
Show Answer & Explanation

Answer: (c) 2.75 × 10⁶ m⁻¹

Explanation:
1. Last line is the series limit: wave number = R/4 = 2.75 × 10⁶ m⁻¹.

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

Question 18: The angular momentum of the electron in hydrogen atom in the ground state is
(a) \( 2h \)
(b) \( \frac{h}{2} \)
(c) \( \frac{h}{2\pi} \)
(d) \( \frac{h}{4\pi} \)
Show Answer & Explanation

Answer: (c) \( \frac{h}{2\pi} \)

Explanation:
1. L = nh/2π with n = 1 gives h/2π.

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

Question 19: In an atom, the two electrons move round the nucleus in circular orbits of radii R and 4R. The ratio of the time taken by them to complete one revolution is
(a) 1/4
(b) 4/1
(c) 8/1
(d) 1/8
Show Answer & Explanation

Answer: (d) 1/8

Explanation:
1. r ∝ n², so n = 1 and 2.
2. T ∝ n³, so T₁ : T₂ = 1 : 8.

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

Question 20: In which of the following series does the 121.5 nm line of the hydrogen atom lie?
(a) Lyman series
(b) Balmer series
(c) Paschen series
(d) Brackett series
Show Answer & Explanation

Answer: (a) Lyman series

Explanation:
1. 121.5 nm is the first line (2 → 1) of the Lyman series, in the ultraviolet.

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

Question 21:
Assertion (A): In Lyman series, the ratio of minimum and maximum wavelength is 3/4.
Reason (R): Lyman series constitute spectral lines corresponding to transition from higher energy levels to ground state of hydrogen atom.
(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. λmin = 1/R (n = ∞) and λmax = 4/3R (n = 2).
2. The ratio is 3/4, and it follows because the series ends on n = 1.

Teacher's Note:
1. Use the series limit and the first line.

Question 22: The first model of atom was proposed by
(a) Hans Geiger
(b) Ernst Rutherford
(c) J.J. Thomson
(d) N.H.D Bohr
Show Answer & Explanation

Answer: (c) J.J. Thomson

Explanation:
1. J.J. Thomson proposed the first (plum pudding) model of the atom.

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

Question 23: A 15.0 eV photon collides with and ionizes a hydrogen atom. If the atom was originally in the ground state (ionization potential = 13.6 eV), what is the kinetic energy of the ejected electron?
(a) 1.4 eV
(b) 13.6 eV
(c) 15.0 eV
(d) 28.6 eV
Show Answer & Explanation

Answer: (a) 1.4 eV

Explanation:
1. K = 15.0 − 13.6 = 1.4 eV.

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

Question 24: According to Bohr's model of hydrogen atom
(a) the linear velocity of the electron is quantised
(b) the angular velocity of the electron is quantised
(c) the linear momentum of the electron is quantised
(d) the angular momentum of the electron is quantised
Show Answer & Explanation

Answer: (d) the angular momentum of the electron is quantised

Explanation:
1. Bohr's condition is mvr = nh/2π.

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

Question 25: Rutherford's nuclear model could not explain I. Why atoms emit light of only discrete wavelengths II. How could an atom as simple as hydrogen consisting of a single electron and a single proton, emit a complex spectrum of specific wavelengths
(a) I only
(b) II only
(c) I and II
(d) None of these
Show Answer & Explanation

Answer: (c) I and II

Explanation:
1. The model cannot explain atomic line spectra nor the stability of the atom.

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

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