A small plate of a metal (work function `=1.7eV`) is placed at a distance of 2m from a monochromatic light source of wavelength `4.8xx10^(-7)m` and power 1.0watt. The light falls normally on the plate. Find the number of protons striking the metal plate per square metre per second. If a constant magnetic field of strength `10^(-4)T` is applied parallel to the metal surface, find the radius of the largest circular path followed by the emitted photoelectron. (use `h=6.63xx10^(-34)Js` , mass of electron=`9.1xx10^(-31)kg`, charge of electron=`1.6xx10^(-19)C`

Explanation

Photon energy `=(hc)/lambda=((6.6xx10^(-34))xx(3xx10^(8)))/(4.8xx10^(-7))`
`=4.125xx10^(-19)J`
The rate of emission of photon from the source
`=(1.0Js^(-1))/(4.125xx10^(-19)J)=2.425xx10^(18)s^(-1)`
No. of photon striking per square meter per second on the metal plate
`=(2.425xx10^(18))/(4pir^(2))=(2.425xx10^(18))/(4xx(3.14)xx(2)^(2))=4.82xx10^(16)`
The maximum K.E. (K) of the photoelectrons emitted from the plate having work function `phi_(0)(=1.17eV)` is given by
`K_(max)=(hc)/lambda-phi_(0)`
`=(4.125xx10^(-19)J)-(1.17xx1.6xx10^(-19)J)`
`=2.253xx10^(-19)J`
The maximum velocity of photoelectrons
`v_(max)=sqrt((2K_(max))/m)=sqrt((2xx2.253xx10^(-19))/(9.1xx10^(-31)))`
`=7.036xx10^(5)ms^(-1)`
The radius of the largest circle traversed by photoelectron in magnetic field B in given by
`r_(max)=(mv_(max))/(eB)=((9.1xx10^(-31))xx(7.036xx10^(5)))/((1.6xx10^(-19))xx(10^(-4)))`
`=0.04m=4.0cm`