Which of the following statements about the Bohr model of the hydrogen atom is false? (a) Acceleration of electron in n = 2 orbit is less than that in n = 1 orbit. (b) Angular momentum of electron in n = 2 orbit is more than that in n = 1 orbit. (c) Kinetic energy of electron in n = 2 orbit is less than that in n = 1 orbit. (d) Potential energy of electron in n = 2 orbit is less than that in n = 1 orbit.

Answer: (d). (a) a = v²/r with v ∝ 1/n, r ∝ n², so a ∝ 1/n⁴: smaller for n = 2. True. (b) L = (nh)/(2π) is larger for n = 2. True. (c) K = (13.6)/(n²) eV: 3.4 eV < 13.6 eV. True. (d) U = -(27.2)/(n²) eV: U₂ = -6.8 eV is greater than U₁ = -27.2 eV, not less. False. So the answer is (d).

Which of the following statements about the Bohr model of the… | MHT CET 2024 (2 May, Shift 2)

Q17MHT CET 2024 · 2 MAY · SHIFT 2Medium

Energy of the Electron & Energy Levels

Which of the following statements about the Bohr model of the hydrogen atom is false?

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Answer: (d)

(a) $a = \frac{v^2}{r}$ with $v \propto \frac{1}{n}$ , $r \propto n^2$ , so $a \propto \frac{1}{n^4}$ : smaller for $n = 2$ . True.
(b) $L = \frac{nh}{2\pi}$ is larger for $n = 2$ . True.
(c) $K = \frac{13.6}{n^2}$ eV: $3.4$ eV $< 13.6$ eV. True.
(d) $U = -\frac{27.2}{n^2}$ eV: $U_2 = -6.8$ eV is greater than $U_1 = -27.2$ eV, not less. False.
So the answer is (d).

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