Question

the time taken by the electron is one complete revolution in the nth bohrs orbit of the hydrogen atom is.?

Answer 1

this is the answer of the question time taken by an electron in one second

Answer 2

Answer:

The time taken by the electron to complete 1 revolution in the nth Bohr orbit of the hydrogen atom is :

$T=1.534\times 10^{-10}\times \frac{n^3}{Z^2}$ seconds

Explanation:

Velocity of an electron in nth shell = $V_n$

Displacement of an electron in complete revolution = $2\pi r_n$

Time taken by an electron to complete one revolution in nth shell = T

$Velocity=\frac{Displacement}{time}$

$V=\frac{2\pi r_n}{T}$

$T=\frac{2\pi r_n}{V_n}$

Velocity of an electron in an nth shell is given by:

$V_n=2.165\times 10^6\times \frac{Z}{n}$

Radius of nth shell is given by:

$r_n=\frac{n^2\times 5.29\times 10^{-11}}{Z}$ (in meter)

where,

n = number of orbit

Z = atomic number

$T=\frac{2\pi \frac{n^2\times 5.29\times 10^{-11}}{Z}}{2.165\times 10^6\times \frac{Z}{n}}$

Time taken by an electron to complete one revolution in nth shell:

$T=1.534\times 10^{-10}\times \frac{n^3}{Z^2}$ seconds