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

Answer

A

Explanation

`(hc)/(lambda_(ph))+eV - phi = (P_(max)^(2))/(2m)`
`rArr (hc)/(lambda_(ph))+eV -phi =(h^(2))/(2mlambda_(e)^(2))`
for `V gt gt phi/e`
`rArr phi lt lt eV and (hc)/(lambda_(Ph)) lt lt eV `
`rArr eV = (h^(2))/(2mlambda_(e)^(2))`
`rArr lambda_(e) prop 1/(sqrt(V))`
Hence , when V is made four times `lambda_(e )` is halved .