Verified Solution • 2025–26 Session moderate

QPages 384-386: Q42: HC Verma: Concepts of Physics - Volume 2 Bohr's Model and Physics of the Atom Pages 384-386: Q42 Solution: The earth revolves round the sun due to gravitational…

The earth revolves round the sun due to gravitational attraction. Suppose that the sun and the earth are point particles with their existing masses and that Bohr's quantization rule for angular momentum is valid in the case of gravitation. a) Calculate the minimum radius the earth can have for its orbit. b) What is the value of the principal quantum number nn for the present radius? Mass of the earth = 6.0×10−24 kg6.0 \times 10^{-24} \text{ kg}. Mass of the sun = 2.0×1030 kg2.0 \times 10^{30} \text{ kg}, earth-sun distance = 1.5×1011 m1.5 \times 10^{11} \text{ m}.

Step-by-Step Verified Solution

**Answer:** (a) r_min = 2.3 _ 10____ m (b) n = 2.5 _ 10__. **Step-by-Step Explanation:** Using Bohr's quantization for gravitational system:
mvr=nh2πmvr = \frac{nh}{2\pi}
For minimum radius, n=1:
r=h24π2GMm2r = \frac{h^2}{4\pi^2 G M m^2}
M = 2 _ 10__ kg (sun), m = 6 _ 10__ kg (earth). r = (6.63 _ 10___)_ / (4�_ _ 6.67 _ 10___ _ 2 _ 10__ _ (6 _ 10__)_) = 2.3 _ 10____ m. (b) For r = 1.5 _ 10__ m: n = sqrt(r/r_min) = 2.5 _ 10__ [citation:3].

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