Light of wavelength `lambda_(ph)`falls on a cathode plate inside a vacuum tube as shown in the figure .The work function of the cathode surface is `phi` and the anode is a wire mesh of conducting material kept at distance d from the cathode. A potential different V is maintained between the electrodes. If the minimum de Broglie wavelength of the electrons passing through the anode is `lambda_(e) ` which of the following statement (s) is (are) true?

Options

A. `lambda_(e ) ` decreases with increase in `phi` and `lambda_(ph)`
B. `lambda_(e ) ` is approximately halved, if d is doubled
C. For large potential difference `( V gt gt phi //e ) , lambda_(e ) ` approximately halved if V is made four time
D. `lambda_(e ) ` increases at the same rate as `phi_(ph )` for `lambda_(ph) lt hc //phi`

Answer

C