The graph between `1//lambda` and stopping potential (V) of three metals having work- functions `Phi_1`, `Phi_2` and `Phi_3` in an experiment of photoelectric effect is plotted as shown in the figure. Which of the following statement(s) is/are correct? (Here, `lambda` is the wavelength of the incident ray). (a) Ratio of work functions `phi_1 : phi_2 : phi_3 = 1 : 2 : 4` (b) Ratio of work functions `phi_1 : phi_2 : phi_3 = 4 : 2 : 1` (c ) tan `theta` is directly proportional to hc / e, where h is Planck constant and c is the speed of light (d) The violet colour light can eject photoelectrons from metals 2 and 3 .

Answer

A, B, C, D

Explanation

From the relation, `eV = (hc)/(lambda) - phi or V= ((hc)/(e )) ((1)/(lambda)) - (phi)/(e ) `
This is equation of straight line. Slope is tan `theta = (hc)/(e )`
Further `V = 0 at phi = (hc)/(lambda)`
`:. phi_1 : phi_2 : phi_3 = (hc)/(lambda_(01) : (hc)/(lambda_(02) :(hc)/(lambda_(03) = (1)/(lambda_01) : (1)/(lambda_02) : (1)/(lambda_03): = 1:2:4`
`(1)/(lambda _(01) = 0.001 nm^(-1) or lambda _(-01) = 10000 Å`
`(1)/(lambda _(02) = 0.002 nm^(-1) or lambda _(-02) = 5000 Å`
(1)/(lambda _(03) = 0.004 nm^(-1) or lambda _(-03) = 2500 Å`
Violet colour has wavelength `4000 Å`
So, violet colour can eject photoelectrons from metal 1 and metal 2.
`:.` The correct option are (a) and (c ).