The work function (W0) of Li , K , Mg , Ag and Cu are 2.42,2.25,3.70,4.30 and 4.80 eV respectively. The number of metals which undergo photoelectric effect if a radiation of wavelength 540 nm falls on them is (1 eV =1.602 × 10-19 J )

Question

The work function (W0) of Li , K , Mg , Ag and Cu are 2.42,2.25,3.70,4.30 and 4.80 eV respectively. The number of metals which undergo photoelectric effect if a radiation of wavelength 540 nm falls on them is (1 eV =1.602 × 10-19 J ) (A) 4 (B) 2 (C) 1 (D) 3

Tardigrade Admin · Accepted Answer

For any metal to show photoeiectric effect,

v > v_{0}

, where

v_{0}

is threshold frequency,

v

is the frequency of light.

Given,

W_{0}

of

L i = 2.42 e V = 2.42 \times 1.602 \times 1 0^{- 19} J

= 3.876 \times 1 0^{- 19} J

W_{0}

of

K = 2.25 e V = 3.604 \times 1 0^{- 19} J

W_{0}

of Mg

= 3.70 e V = 5.927 \times 1 0^{- 19} J

W_{0}

of

A g = 4.30 e V = 6.888 \times 1 0^{- 19} J

W_{0}

of

C u = 4.80 e V = 7.689 \times 1 0^{- 19} J

Also

W_{0} = h v_{0}

∵ v_{0}

of

L i = W_{0} / h

= \frac{3.876 \times 1 0 ^{- 19}}{6.626 \times 1 0 ^{- 34}} = 0.584 \times 1 0^{15} s^{- 1}

∴ v_{0}

of

K = \frac{W _{0}}{h} = \frac{3.604 \times 1 0 ^{- 19}}{6.626 \times 1 0 ^{- 34}}

= 0.54 \times 1 0^{15} s^{- 1}

∴ v_{0}

of

M g = \frac{5.927 \times 1 0 ^{- 19}}{6.626 \times 1 0 ^{- 34}} = 0.89 \times 1 0^{15} s^{- 1}

∴ v_{0}

of

A g = \frac{6.888 \times 1 0 ^{- 19}}{6.626 \times 1 0 ^{- 34}} = 1.03 \times 1 0^{15} s^{- 1}

v_{0}

of

C u = \frac{7.689 \times 1 0 ^{- 19}}{6.626 \times 1 0 ^{- 34}}

= 1.16 \times 1 0^{15} s^{- 1}

Frequency of light can be calculated as:

v = \frac{c}{λ}

= \frac{3 \times 1 0 ^{8}}{540 \times 1 0 ^{- 9}} = 0.0056 \times 1 0^{17} s^{- 1}

\approx 0.56 \times 1 0^{15} s^{- 1}

Thus, only in case of

K, v > v_{0}

thus it will show photoelectric effect

Q. The work function (W0​) of Li,K,Mg,Ag and Cu are 2.42,2.25,3.70,4.30 and 4.80eV respectively. The number of metals which undergo photoelectric effect if a radiation of wavelength 540nm falls on them is (1eV=1.602×10−19J)

4

2

1

3

Q. The work function $(W_{0})$ of $L i, K, M g, A g$ and Cu are $2.42, 2.25, 3.70, 4.30$ and $4.80 e V$ respectively. The number of metals which undergo photoelectric effect if a radiation of wavelength $540 nm$ falls on them is $(1 e V = 1.602 \times 1 0^{- 19} J)$