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

`(hc)/(lambda)=phi+K_(max) =phi+(1)/(2)mv_(max)^(2)`
`mv_(max)^(2) =2((hc)/(lambda) - phi)`
To move in circle, necessary centripetal force is provided by electric force
`(mv_(max)^(2))/(d) =(1)/(4pi in_(0))(e.e)/(d^(2))`
`2((hc)/(lambda) -phi) = (e^(2))/(4pi in_(0)d)`
`(hc)/(lambda) -phi =(e^(2))/(8pi in_(0)d)`
`(hc)/(lambda) =(e^(2))/(8pi in_(0)d)+phi`
`lambda=(hc)/(((e^(2))/(8pi in_(0)d) +phi))`