When light of wavelength 300 nm (nanometer) falls on a photoelectric emitter, photoelectrons are just liberated. For another emitter, however, light of 600 nm wavelength is sufficient for creating photoemission. What is the ratio of the work function of the two emitters?

Question

When light of wavelength 300 nm (nanometer) falls on a photoelectric emitter, photoelectrons are just liberated. For another emitter, however, light of 600 nm wavelength is sufficient for creating photoemission. What is the ratio of the work function of the two emitters? (A)  1:2  (B)  2:1  (C)  4:1  (D)  1:4

Tardigrade Admin · Accepted Answer

The minimum energy required for the emission of photoelectrons from a metal is called the work function of that metal.
Given by

W = h v \dots

(i)
where

v

is threshold frequency and

h

is Planck's constant.
Also,

v = \frac{c}{λ}

...(ii)
where

c

is speed of light and

X

the threshold wavelength.
From Eqs. (i) and (ii), we get

W = \frac{h c}{λ}

Given,

λ_{1} = 300 nm, λ_{2} = 600 nm

∴ \frac{λ _{2}}{λ _{1}} = \frac{W _{1}}{W _{2}}

\Rightarrow \frac{W _{1}}{W _{2}} = \frac{600}{300} = \frac{2}{1}

Q. When light of wavelength $300 nm$ (nanometer) falls on a photoelectric emitter, photoelectrons are just liberated. For another emitter, however, light of $600 nm$ wavelength is sufficient for creating photoemission. What is the ratio of the work function of the two emitters?

$1 : 2$

$2 : 1$

$4 : 1$

$1 : 4$

Q. When light of wavelength 300nm (nanometer) falls on a photoelectric emitter, photoelectrons are just liberated. For another emitter, however, light of 600nm wavelength is sufficient for creating photoemission. What is the ratio of the work function of the two emitters?

1:2

2:1

4:1

1:4

Q. When light of wavelength $300 nm$ (nanometer) falls on a photoelectric emitter, photoelectrons are just liberated. For another emitter, however, light of $600 nm$ wavelength is sufficient for creating photoemission. What is the ratio of the work function of the two emitters?

$1 : 2$

$2 : 1$

$4 : 1$

$1 : 4$