A photon of energy E ejects a photoelectron from a metal surface whose work function is `W_(0)` .If this electon entres into a uniform magnetic field of induction B in a direction perpendicular to the field and describe a circular path of radius r, then the radius r is given by ,(in the usual notation)

Options

A. `sqrt(2m(E-W_(0)))/(eB`
B. `sqrt(2m(E-W_(0))eB`
C. `sqrt(2e(E-W_(0)))/(mB`
D. `sqrt(2m(E-W_(0)))/(eB`

Answer

D

Explanation

From Einstein is equation,`E=w_(o)+(1)/(2)mv^(2)`
" ` v"= sqrt(2(E-W_(0)))/m`
The force required by an electron to enter a magnetic is given by,
" `F" =(mv^(2))/r`
`impliesr=(mv^(2))/F=(mv^(2))/(eBv)=(mv)/(eB)`
`impliesr=msqrt((2(E-W_(o)))/(m))/(eb`
`therefore r=sqrt((2m(E-W_(0)))/(eB`