Each metal is illuminated with 400 nm (3.10 eV) light. Rank the metals on the basis of the maximum kinetic energy of the emitted electrons. (If no electrons are emitted from a metal, the maximum kinetic energy is zero, so rank that metal as smallest.) Rank from largest to smallest. To rank items as equivalent, overlap them.

K. E (K) > K. E (Cs) > 0 (others)

Explanation:

Given the Work functions of the metal as

Aluminium (Wo) = 4eV

Platinum (Wo) = 6.4eV

Cesium (Wo) = 2.1eV

Beryllium (Wo) = 5.0eV

Magnesium (Wo) = 3.7eV

Potassium (Wo) = 2.3eV

Using the formula:

K. E = hf - Wo ... (1)

Wo = hfo ... (2)

From these the fo can be calculated for all the metals

Where K. E = Kinetic Energy

hf = energy of illumination = 3.10eV

h is Planck constant and has the value 6.6 * 10^-34JS^-1

The frequency f of the illumination is given by

f = 3.10 * 1.6 * 10^-19/6.6 * 10^-34

f = 7.51 * 10¹⁴ Hz ... (*)

Now an electron is only ejected if the threshold frequency of the metal is reached.

The work function has a threshold frequency (fo) for all the metals and this minimum frequency required to required to remove an electron from the surface of a metal.

We need to compare f with fo

If fo > = f there is emission, otherwise there is no emission

So using (2) we calculate for all fo and compare with f

K. E (Al) = 3.10 - 4.0 - 3.10 = - 0.9eV, fo = 9.70 * 10¹⁴ Hz (no emission)

K. E (Pt) = 3.10 - 6.40 = - 3.30eV, fo = 1.55 * 10^15 Hz, (no emission)

K. E (Cs) = 3.10 - 2.10 = - 1.0eV, fo = 5.09*10¹⁴ Hz, (emission)

K. E (Be) = 3.10-5.0 = - 1.90eV, fo = 12.12 * 10^15 Hz., (no emission)

K. E (Mg) = 3.10-3.70 = - 0.6eV, fo = 8.97 * 10¹⁴Hz, (no emission)

K. E (K) = 3.10 - 2.30 = 0.9eV, fo = 5.58 * 10¹⁴ Hz, (emission)

So the metals whose electron gain Kinetic energy are:

Cesium

Potassium

Others have zero kinetic energy since no electron is emitted.

Hence the rank is:

K. E (K) > K. E (Cs) > 0 (others)