In accordance with the Bohr’s model, find the quantum number that characterises the earth’s revolution around the sun in an orbit of radius 1.5 × 10¹¹ m with orbital speed 3 × 10⁴ m/s. (Mass of earth = 6.0 × 10²⁴ kg.)

Rdius of the orbit of the Earth around the Sun, r= 1.5 x 10¹¹ m

Orbital speed of the Earth, v = 3 x 10⁴ m/s

Mass of the Earth, m = 6.0 x 10²⁴ kg

According to Bohr’s model, angular momentum is quantized and given as:

mvr = nh/2π

Where,

h = Planck’s constant = 6.62 x 10⁻³⁴ Js

n = Quantum number

Therefore , n = mvr2π/h

= 2π x (6.0 x 10²⁴ ) x (3 x 10⁴ ) x (1.5 x 10¹¹) /(6.62 x 10⁻³⁴)

= 25.61 x 10⁷³= 2.6 x 10⁷⁴

Hence, the quanta number that characterizes the Earth’ revolution is 2.6 x 10⁷⁴.