An electron in hydrogen atom stays in its second orbit for 10 s. How many revolutions will it make around the nucleus in that time?

Question

An electron in hydrogen atom stays in its second orbit for 10^-8 s. How many revolutions will it make around the nucleus in that time?

Answer 1

Data : z = 1, m = 9.1 × 10^-31 kg, 

e = 1.6 × 10^-19 C, 

ε_o = 8.85 × 10^-12 C² / N.m² , 

h = 6.63 × 10^-34 J.s, 

n = 2, t = 10^-8 s 

The periodic time of the electron in a hydrogen atom,

T = \(\cfrac{4e^2_oh^3n^3}{\pi me^4}\)

Let N be the number of revolutions made by the electron in time t. Then, t = NT.

∴ N = \(\cfrac{t}T\) = \(\cfrac{10^{-8}}{3.898\times10^{-16}}\) = 2.565 x 7