Speed of electron in its 1st Bohr's orbit is given by `2.18xx 10^(6) ms^(-1)` . It the time period of electron in n th orbit is measured as 4.10 femto second, the value of n is

Options

A. 1
B. 2
C. 3
D. 4

Answer

C

Explanation

Given speed of the electron in 1st Bohr.s orbit
`v_(1) =2.18xx 10^(6) m//s`
Time period of nth orbit
`T_(n) = 4.10 f = 4.1 xx 10^(15) s`
Radius of Bohr.s first orbit `r_(1) = 0.53 xx 10^(-19) m`
Orbital period of electron in Bohr.s first orbit
`T_(1) = (2pi r^(1))/( v_(1)) = (2xx 314 xx 0.53 xx 10^(-10))/(2.18 xx 10^(6))`
Again Time period of n th orbit is given by
`T_(n) = n^(3) T_(1)`
`rArr n^(3) = (T_(n))/(T_(1)) = (4.1 xx 10^(15))/( 1.52 xx 10^(-18)) = 26.98 `
`n^(3) =27 rArr n= (27)^(1//3) rArr n=3`