Question

When blue light (450 nm) is shone on a particular metal surface, electrons are ejected with a kinetic energy of 2.5 x 10-20 J. Calculate the work function for this metal.

Answer 1

Answer:

the work function of the metal is 4.167 x 10⁻¹⁹ J .

Explanation:

Given;

wavelength of the incident light, λ = 450 nm = 450 x 10⁻⁹ m

kinetic energy, K.E = 2.5 x 10⁻²⁰ J

The energy of the incident light is calculated as;

$E = hf = \frac{h c}{\lambda} \\\\where;\\\\c \ is \ speed \ of \ light = 3 \times 10^8 \ m/s\\\\ h \ is \ Planck's constant = 6.626 \times 10^{-34} Js \\\\E = \frac{(6.626 \times 10^{-34})(3\times 10^8)}{450 \times 10^{-9}} \\\\E = 4.417 \times 10^{-19} \ J$

Apply Einstein photoelectric equation to determine the work function of the metal;

E = W + K.E

where;

W is the work function of the metal

W = E - K.E

W = 4.417 x 10⁻¹⁹ J - 2.5 x 10⁻²⁰ J

W = 44.17 x 10⁻²⁰ J -  2.5 x 10⁻²⁰ J

W = 41.67 x 10⁻²⁰ J

W = 4.167 x 10⁻¹⁹ J

Therefore, the work function of the metal is 4.167 x 10⁻¹⁹ J .