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

Answer

C

Explanation

Let the largest radius of the circular path followed by electron be r
`(mv^2)/r=evB`
`impliesv=((reB)/m)`
Energy of the photon emitted by transition of electron.
`E=13.6[1/4-1/9]eV=1.89eV`
`E=phi+K.E._(max)`
`1.89=phi+1/2mv^2`
`implies1.89=phi+1/2m((reB)/m)^2xx1/e`
`impliesphi=1.89-1/2((10xx10^(-3))^2xx(1.6xx10^(-19))^2xx(3xx10^(-4))^2)/(9.1xx10^(-31)xx1.6xx10^(-19))`
`implies phi=(1.89-0.79)eV`
`:. phi=1.1 eV`