Question

A photon of wavelength 4×10^–7 m strikes on metal surface, the work function of the metal being 3×10^–19 J.

Calculate

(i) The energy of the photon (in Joules)

(ii) The kinetic energy of the emitted electron ​

Answer 1

Given :-

◉ A photon of wavelength λ = 4 × 10⁻⁷ m

◉ A metal surface, whose work function is 3 × 10⁻¹⁹ J

To Find :-

◉ Energy of the photon (in Joules)

◉ Kinetic energy of the emitter electron.

Solution :-

We know, Energy of the photon must be greater than the work function in order to eject electron from the metal surface.

⇒ E = hc / λ

Where,

• h = Planck's constant

= 6.6 × 10⁻³⁴

• c = Speed of Light

= 3 × 10⁸

• λ = Wavelength

= 4 × 10⁻⁷ m

⇒ E = (6.6 × 10⁻³⁴ × 3 × 10⁸) / (4 × 10⁻⁷)

⇒ E = 1.65 × 3 × 10⁻²⁶ × 10⁷

⇒ E = 4.95 × 10⁻¹⁹ Joules

Hence, The energy of the photon is 4.95 × 10⁻¹⁹ Joules.

Now, We need to find the kinetic energy of the emitted electron. But, we are given the work function of the metal. So,

⇒ K.E of emitted electron = Energy of Photon - Work function

⇒ K.E = 4.95 × 10⁻¹⁹ - 3 × 10⁻¹⁹

⇒ K.E = 10⁻¹⁹ (4.95 - 3)

⇒ K.E = 1.95 × 10⁻¹⁹ Joules

Therefore, Kinetic energy of the emitted electron is 1.95 × 10⁻¹⁹ Joules.