A small metal plate is kept at a distance d form a singly ionized, fixed ion. A monochromatic light beam is incident on the metal plate and photoelectrons are emitted. Find the maximum wavelength of the light beam so that some of the photoelectrons may go round the ion along a circle.

Explanation

Electron is moving around the ion in a Circle of radius .d.. Centripetal force is provided by Electrostatic force
`(1)/(4piepsi_(0))(e^(2))/(d^(2))=(mV^(2))/(d),:.mV^(2)=(1)/(4piepsi_(0))(e^(2))/(d)`
`:.K.E=(1)/(8piepsi_(0))(e^(2))/(d)" ".......(1)`
But `K.E_(max)=(hc)/(lamda)-W" "......(2)`
`:.(hc)/(lamda)-W=(e^(2))/(8piepsi_(0)d)`
`:.lamda=(hc8piepsi_(0)d)/(e^(2)+8piepsi_(0)dW)`