The velocity of electron v in the second orbit of hydrogen, then its velocity in the fifth orbit will be ......

Options

A. `(5)/(7)v`
B. `(7)/(5)v`
C. `(2)/(5)v`
D. `(5)/(2)v`

Answer

C

Explanation

The velocity of electron in `n^(th)` orbit of H atom
`vecv_(n)=(Ze^(2))/(2in_(0)nh)`
But for H,Z=1 and `(e^(2))/(2in_(0)h)` constant
`:.v_(n)prop(1)/(n)`
`:.(v_(5))/(v_(2))=(2)/(5)`
`:.v_(5)=(2)/(5)v_(2)`
`:.v_(5)=(2)/(5)v" "[:.v_(2)=v]`