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)propto n^(2)`
`(r_("n big"))/r_("n small")=(n^(2)big)/("n^(2)small)=4/1 ` (given)
Rightarrow`n_(big)/n_(small)=2`
Rightarrow`n_(small)/n_(big)=1/2`
Velocity of electron in nth orbit
`v_(n)propto1/n`
`v_"(n big)"/(v_"(n small)" )=(n_(small))/n_(big)=1/2`
Rightarrow`V_"n small"=2(v_"n big")=2v`