In hydrogen atom, an electron jumps from bigger orbit to smaller orbit, so that radius of smaller orbit is one-fourth of radius of bigger orbit. If speed of electron in bigger orbit was v,then speed in smaller orbit is

Options

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

Answer

D

Explanation

Radius of nth orbit
`r_(n) prop n^(2)`
`(r_("n bigger"))/(r_("n small"))=(n_("bigger")^(2))/(n_("smaller")^(2))=(4)/(1)`
`implies (n_("bigger"))/(n_("smaller"))=2 implies (n_("smaller"))/(n_("bigger"))=(1)/(2)`
Velocity of electron in nth orbit,
`v_(n)prop(1)/(n) implies (v_("n bigger"))/(v_("v smaller"))=(n_("smaller"))/(n_("bigger"))=(1)/(2)`
`implies v_("n smaller")=2(v_("n bigger"))=2v`