Question 218: Dual Nature of Matter and Radiation

Question

A photoelectric surface is illuminated successively by monochromatic light of wavelengths $$\lambda $$ and $${\lambda  \over 2}.$$ If the maximum kinetic energy of the emitted photoelectrons in the second case is 3 times that in the first case, the work function of the surface is :

Accepted Answer

We know,
Einstein's photo electric equation,
(KE)
max
= $${{hc} \over \lambda }$$ $$-$$ $$\phi $$
0
In first case,
K = $${{hc} \over \lambda }$$ $$-$$ $$\phi $$
0
. . .(1)
In second case,
3K = $${{2hc} \over \lambda }$$ $$-$$ $$\phi $$
0
. . .(2)
$$ \Rightarrow $$   $$3\left( {{{hc} \over \lambda } - {\phi _0}} \right)$$ = $${{2hc} \over \lambda } - {\phi _0}$$
$$ \Rightarrow $$   $${{3hc} \over \lambda }$$ $$-$$ 3$$\phi $$
0
= $${{2hc} \over \lambda }$$ $$-$$ $$\phi $$
0
$$ \Rightarrow $$   $${{hc} \over \lambda }$$ = 2$$\phi $$
0
$$ \Rightarrow $$   $$\phi $$  =  $${{hc} \over {2\lambda }}$$

Answer

$${{hc} \over {3\lambda }}$$

Answer

$${{hc} \over {2\lambda }}$$

Answer

$${{hc} \over {\lambda }}$$

Answer

$${3\,{hc} \over {\lambda }}$$

Dual Nature of Matter and Radiation

A photoelectric surface is illuminated successively by monochromatic light of wavelengths $\lambda and {\lambda \over 2}.$ If the maximum kinetic energy of the emitted photoelectrons in the second case is 3 times that in the first case, the work function of the surface is :

Choose the correct answer: