An electrons is moving in Bohr's fourth orbits De-Broglie wavelength s `lambda`.What is the circumference of the fourth orbit?

Options

A. `2/lambda`
B. `2lambda`
C. `4lambda`
D. `4/lambda`

Answer

c

Explanation

According to Bohr.s theory, the angular momentum of an electron in the orbit is given by,
`m_ev_r=(nh)/(2pi)`
`r=n/(2pi)xxh/(mv) (therefore lambda=h/(mv))`
`=(nlambda)/(2pi)`
an electron is moving in fourth orbit i.e,n=4
then `r=(4lambda)/(2pi)=(2lambda)/(pi)therefore` circumference of the orbit `=2pir`
By subsituting eq. (1) in (2), we get
Circumference of orbit `-2pixx(2lambda)/R=4ambda`