The radiation corresponding to ` 3 rarr 2` transition of hydrogen atom falls on a metal surface to produce photoelectrons . These electrons are made to enter circuit a magnetic field `3 xx 10^(-4) T` if the ratio of the largest circular path follow by these electron is `10.0 mm , the work function of the metal is close to

Options

A. `1.8eV`
B. `1.1 eV`
C. `0.8eV`
D. `1.6 eV`

Answer

B

Explanation

Radius of circular path followed by electron is given by
` r= (mv )/( q B ) = ( sqrt(2 me V )/( eB )) = (1)/(B ) sqrt((2m )/(e ) V)`
`implies V =(B^2 r^2 e )/(2m ) = 0. 8 V `
for transition between 3 to 2 .
`E= 13.6 (1/4-1/9) = ( 13.6 xx 5 )/( 36 )= 1.88 eV `
Work function `= 1.88 eV - 0.8 eV = 1.08 eV ~~ 1.1 eV `