Question

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)

Answer 1

Radius of the orbit of the Earth around the Sun, r = 1.5 × 10¹¹ m

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

Mass of the Earth, m = 6.0 × 10²⁴ kg

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

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

Where,

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

n = Quantum number

∴ `"n" = ("mvr" 2pi)/"h"`

= `(2pi xx 6 xx 10^24xx 3 xx 10^4 xx1.5 xx 10^(11))/(6.62 xx 10^(-34))`

= 25.61 × 10⁷³

= 2.6 × 10⁷⁴

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