Question

The earth revolves around the sun in an orbit of radius 1.5 × 10¹¹ m with orbital speed 30 km/s. Find the quantum number that characterises its revolution using Bohr’s model in this case (mass of earth = 6.0 × 10²⁴ kg).

Answer 1

Given, r = 1.5 × 10¹¹ m

v = 3 × 10⁴ m/s

m = 6.0 × 10²⁴ kg

According to Bohr's model, angular momentum is given as,

`mvr = (nh)/(2pi)`

⇒ `n = (mvr2pi)/h`

= `(6 xx 10^24 xx 3 xx 10^4 xx 1.5 xx 10^11 xx 2 xx 3.14)/(6.626 xx 10^-34)`

⇒ n ≃ 3.0 × 10⁷⁴