Nuclear Radius

Q5.

(a) On the graph paper below sketch a graph to show how the radius, R, of a nucleus varies with its nucleon number, A.

You need to sketch a graph starting (steeply) near/at the origin and decreasing in gradient

It is rather misleading that they used graph paper as you may have thought you would have to mark values on the axes - not needed!

(1 mark)

(b) The radius of a gold-197 nucleus is 6.87 × 10^–15 m.

(i) Show that the density of this nucleus is about 2.4 × 10¹⁷ kg m^–3.

 

mass = 197 x 1.67 x 10^-27= 3.29 x 10^-25 kg

volume = 4/3 (πr³) = 4π x (6.87 × 10^–15)³ /3 = 1.39 x 10^-42 m³

density = mass/volume = 2.4 × 10¹⁷ kg m^-3

(2 marks)

(ii) Using the data from part b(i) calculate the radius of an aluminium-27 nucleus, .

R_Al³/A_Al = R_Au³/A_Au

R_Al³= R_Au³A_Al/A_Au

R_Al³= (6.87 × 10^–15)³x 27/197

R_Al= 3.54 x 10^-15m

Or substitute into the equation... Or use the fact that the density will be the same

(2 marks)

(c) Nuclear radii have been investigated using α particles in Rutherford scattering experiments and by using electrons in diffraction experiments.

Make comparisons between these two methods of estimating the radius of a nucleus. Detail of any apparatus used is not required. This was often ignored!

For each method your answer should contain:

the principles on which each experiment is based including a reference to an appropriate equation

an explanation of what may limit the accuracy of each method

a discussion of the advantages and disadvantages of each method

If you don't include all three of these your answer cannot be high level!

The quality of your written communication will be assessed in your answer.

This means that :

Your writing should be legible and the spelling, punctuation and grammar should be sufficiently accurate for the meaning to be clear. Your answer will be assessed holistically.

The answer will be assigned to one of three levels according to the following criteria.

High Level (Good to excellent): 5 or 6 marks

The information conveyed by the answer is clearly organised, logical and coherent, using appropriate specialist vocabulary correctly. The form and style of writing is appropriate to answer the question.

The candidate makes 5 to 6 points concerning the principles of the method, the limitations to the accuracy and the advantages and disadvantages of a particular method

Intermediate Level (Modest to adequate): 3 or 4 marks

The information conveyed by the answer may be less well organised and not fully coherent. There is less use of specialist vocabulary, or specialist vocabulary may be used incorrectly. The form and style of writing is less appropriate. The candidate makes 3 to 4 points concerning the principles of the method, the limitations to the accuracy and the advantages and disadvantages of a particular method

Low Level (Poor to limited): 1 or 2 marks

The information conveyed by the answer is poorly organised and may not be relevant or coherent. There is little correct use of specialist vocabulary. The form and style of writing may be only partly appropriate. The candidate makes 1 to 2 points concerning the principles of the method, the limitations to the accuracy and the advantages and disadvantages of a particular method

The explanation expected in a competent answer should include a coherent selection of the following points concerning the physical principles involved and their consequences.

Principles

α scattering involves coulomb or electrostatic repulsion

electron diffraction treats the electron as a wave having a de Broglie wavelength

some reference to an equation, for example λ = h/mv ; eV = mv²/2 ; Qq/4πε_or = Eα ; sinθ = 0.61λ/R

reference to first minimum for electron diffraction

Accuracy

α-particles only measure the least distance of approach, not the radius

α-particle have a finite size which must be taken into account

electrons need to have high speed/kinetic energy to have a small wavelength or wavelength comparable to nuclear diameter, the wavelength determines the resolution

the wavelength needs to be of the same order as the nuclear diameter for significant diffraction

requirement to have a small collision region in order to measure the scattering angle accurately

importance in obtaining monoenergetic beams

cannot detect alpha particles with exactly 180^o scattering

need for a thin sample to prevent multiple scattering

Advantages and disadvantages

α-particle measurements are disturbed by the nuclear recoil

mark for α-particle measurements are disturbed by the strong nuclear force when coming close to the nucleus or electrons are not subject to the strong nuclear force.

a second mark can be given for reference to strong nuclear force if they add electrons are leptons or alpha particles are hadrons.

α-particles are scattered only by the protons and not all the nucleons that make up the nucleus

visibility – the first minimum of the electron diffraction is often difficult to determine as it superposes on other scattering events

(6 marks)

(Total 11 marks)