Question

3) The amount of energy it takes to eject an electron from the surface of a metal is 4.15 x 10-19J. If light with a wavelength of 625nm is shined on the metal, what will happen? Prove your answer mathematically by finding the frequency and energy of the wave.

Answer 1

We can use two equations to solve this.
(1) - E = hf
        E = Energy (J)
        h = plank's constant (6.63 × 10⁻³⁴ J s)
        f  = frequency (Hz)

(2) - v = fλ
        v = velocity of the wave (m/s)
       f  = frequency (Hz)
       λ = wavelength (m)

the λ for the given wave is 625nm (625 x 10⁻⁹ m) and the velocity of the wave is equal to speed of light (3 x 10⁸ m/s) since the wave is a light.

hence we can find the frequency of the wave by using (2) formula.
3 x 10⁸ m/s = f x 625 x 10⁻⁹ m
                f  = 4.8 x 10¹⁴ Hz

by using calculated frequency and (1) formula, we can find the energy of the wave.
 E = 6.63 × 10⁻³⁴ J s x 4.8 x 10¹⁴ Hz
 E = 3.18 x 10⁻¹⁹ J

The energy of wave is less than energy needed to eject an electron.
Hence, the metal does not eject electron.