Question

Ratio of time periods of electrons in 1st and 2nd orbits of Hydrogen is?

Answer 1

The time period of an electron is given by,
$T = n^3h^3/(4π^2mZ^2e^4)$
For first orbit, n = 1
$T_1 = 1^3h^3/(4π^2mZ^2e^4)$
For second orbit, n = 2
$T_2 = 2^3h^3/(4π^2mZ^2e^4)$
Therefore, we have
$T_1/T_2 = 1:8$

The time period of an electron can be expressed as follows:

T =n 3 h 34 π 2 mZ 2 e 4​

For the first orbit (n = 1):

T 1​=13 h 34 π 2 mZ 2 e 4​

For the second orbit (n = 2):

T 2​=23 h 34 π 2 mZ 2 e 4​

Consequently,

T 1​ T 2​​=81​

This ratio signifies a proportion of 1 to 8.