On Fig. 10.1, sketch the variation with λ of the maximum kinetic energy EMAX of the electrons emitted from the surface

Question 4

(a) A metal surface is illuminated with light of a single wavelength λ.

On Fig. 10.1, sketch the variation with λ of the maximum kinetic energy EMAX of the electrons emitted from the surface.

On your graph mark, with the symbol λ­₀, the threshold wavelength.

Fig. 10.1

[3]

(b) A neutron is moving in a straight line with momentum p.

The de Broglie wavelength associated with this neutron is λ.

On Fig. 10.2, sketch the variation with momentum p of the de Broglie wavelength λ.

Fig. 10.2

[2]

[Total: 5]

Reference: Past Exam Paper – November 2017 Paper 42 Q10

Solution:

(a)

λ0 marked and graph line passing through EMAX = 0 at λ = λ0

graph line with λ always < λ0                                                                  

negative gradient with correct concave curvature    

{Energy of photon: E = hf = hc / λ

Energy from photon = Work function + KE

Energy is required for the electrons to break free from the metal. The remaining energy goes as kinetic energy.

The minimum energy required to liberate an electron is called the work function which occurs at a threshold frequency f₀ and corresponding threshold wavelength λ₀ (this is the max wavelength for emission. Photons of greater wavelength will not cause emission).

If the energy of the photon is equal to the work function, no energy goes as KE.

→ So, when λ = λ₀, E_MAX = 0.

The threshold wavelength λ₀ is the maximum wavelength for photoemission. Photons of greater wavelength will not cause emission).

→ So, the line is always in the region < λ₀.

Energy of photon: E = hf = hc / λ

KE or E_MAX = Energy of photon – Work function

OR E_MAX = hc / λ  (– Work function)

The E_MAX is inversely proportional to λ. The graph is that of an inverse relationship, having a negative gradient.}

(b)

curve with negative gradient and correct concave curvature           

not touching either axis                                                                      

The de Broglie wavelength and the momentum are related by the equation:

λ = h / p

This is an inverse relationship graph. The graph does not touch either axis.