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

Answer

D

Explanation

In magnetic field, Radius `R=sqrt(2m(K.E.))/(qB)`
`K.E. =(q^(2)B^(2)R^(2))/(2m), K.E.=0.80 eV`
Energy of photon for transition from `3 rarr 2` in hydrogen atom
`E=13.6 [1/2^(2)-1/3^(2)]=1.88 eV`
From Einstein photoelectric equation
`E=K.E_("max") +phi implies 1.88 =0.8+phi`
`implies phi=1.08 eV implies phi ~~ 1.1 ev`