Question

Calculate the orbital period of the electron in the first excited state of h - atom ?

Answer 1

by simplifying formula after putting values of constants

we get

v¹ = 2.18 x {{10}^{6}} m/s

and V = v¹ / n

For first excited state n = 2

so V = (2.18 x {{10}^{6}})/2 m/s

V = 1.09 x {{10}^{6}} m/s

time period = 2 π R°/ V

(radius taken for orbital n=2)

R° = n²r ( r =52.9 pm)

so T = 2× 2² ×52.9 ×10-¹²/ 1.09 x {{10}^{6}}

T =1.22 × 10^-15 seconds....

(short method given in pictures for better understanding)