A small metal plate of work function `phi` is kept at a distance r from a singly ionised, fixed ion. A monochromatic light beam is incident on the metal plate and photoelectrons are emitted. Find maximum wavelength of the light beam so that some of that electrons may go round the ion along a circle.

Explanation

If electron is to move around the ion in circular path of radius r, then
`:. (mv^(2))/r=1/(4pi in_(0)) (e.e)/(r^(2)) or mv^(2)= 1/(4pi in_(0)) (e^(2))/r`
Kinetic energy of electron `=1/2mv^(2)=(e^(2))/(2xx4pi in_(0) r) =(e^(2))/(8pi in_(0) r)`
As `1/2 mv_(max)^(2)=(hc)/(lambda)-phi_(0) :. (e^(2))/(8pi in_(0) r)=(hc)/(lambda)-phi or (hc)/lambda=(e^(2))/(8pi in_(0) r)+phi=(e^(2)+8pi in_(0)r phi)/(2xx4pi in_(0) r)`
`:. lambda=(8pi in_(0)rhc)/(e^(2)+8pi in_(0)rphi)`