Light of wavelength `lambda_(ph)`falls on a plate a vacum teke as shown in the figure .The work function of the conducting meterial kept at a distance d from the cathon A petential different V is maximum between the electrodes if the minimum de Brogle waveleeength of the electrons passing through the anode is `lambda_(e) ` which of the following statement (s) is (are) true?

Options

A. `lambda_(e)`decrease with increase in `phi and lambda_(ph)`
B. `lambda_(e)` is approximentily balved , if d is doubled
C. for large potential diffrence `(Vgtgt phi //e). Lambda_(e) `is approximately halved if V is made four time
D. `lambda_(e) ` increase at the same rate as `lambda_(ph) for lambda_(ph) lt hc//phi`

Answer

C

Explanation

The wavelength of emitted photoelectron as per de brogher is
` lambda_(0) = (h)/(p) = (h)/(sqrt(2m (K.E))`
when `lambda_(ph) increases N_(ph) decreases ` K.E. decreases and therefore I,e increse
let is independent of the decreases d
`Also(hc)/(lambda_(ph)) + eV - phi = (h^(2))/(2m lambda_(00)^(2)) [lambda = (h)/(sqrt(2mK . E))]`
`:. (hc)/(e lambda_(ph)) + V (ph)/(e) = (b^(2))/(2me lambda_(0)^(2)))` ....(i)
`for V gtgt (phi)/(e) , phi ltlt eV`
` also (hc)/(e lambda_(ph)) ltlt V ` Then from eq (i)
`lambda_(e) prop (1)/(sqrt(V))`
Therefore if V is mode our times `lambda_(e)` is approximated half