Question

The work function of some metals is listed below how many of these metals show the Photoelectric effect when the light of $300\mathrm{nm}$ wavelength falls on them?

Metal	K	Na	Li	Mg	Ag	Fe	W	Cu	Pt
ϕ (eV)	2.2	2.3	2.4	3.7	4.3	4.7	4.75	4.8	6.3

• A. Two
• B. Four
• C. Five
• D. None of these

Answer 1

The correct option is B

Four

Explanation for correct option:

(B) Four

Condition for Photoelectric Effect

• The energy of a photon must be higher than the metal's work function for the photoelectric effect to take place.
• The energy of a Photon is given by
• $\mathrm{E}=\frac{\mathrm{hc}}{\mathrm{\lambda }}$

Where,

• $\mathrm{h}-$ Planck's constant
• $\mathrm{c}-$Velocity of light
• $\mathrm{\lambda }-$ Wavelength

Here given that

• $\mathrm{\lambda }=300\mathrm{nm}$

Then,

• $\mathrm{E}=\frac{6.6\times {10}^{-34}\times 3\times {10}^8}{300\times {10}^{-9}}\mathrm{J}$
• $\mathrm{E}(\mathrm{in}\mathrm{eV})=\frac{6.6\times {10}^{-34}\times 3\times {10}^8}{300\times {10}^{-9}\times 1.6\times {10}^{-19}}$
• $\mathrm{E}=4.125\mathrm{eV}$

The metals $\mathrm{Li},\mathrm{Na},\mathrm{K},\mathrm{Mg}$have a work function less than the Energy of a Photon. In the presence of light with a wavelength of$300\mathrm{nm}$, they exhibit a photoelectric Effect.

Therefore, Option (B) Four is correct.

Explanation for the incorrect options:

The four metals show the Photoelectric effect when the light of $300\mathrm{nm}$ wavelength falls on them. Thus, options A, C, and D are incorrect.

Hence, Option (B) Four is correct.