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Date May 2011 Marks available 2 Reference code 11M.2.SL.TZ2.5
Level Standard level Paper Paper 2 Time zone Time zone 2
Command term Draw Question number 5 Adapted from N/A

Question

Part 2 Unified atomic mass unit and a nuclear reaction

Define the term unified atomic mass unit.

[1]
a.
The mass of a nucleus of rutherfordium-254 is 254.1001u. Calculate the mass in GeVc–2.
[1]
b.
In 1919, Rutherford produced the first artificial nuclear transmutation by bombarding nitrogen with αα-particles. The reaction is represented by the following equation. 

α+147N178O+Xα+147N178O+X

(i) Identify X.

(ii) The following data are available for the reaction.

        Rest mass of αα = 3.7428 GeVc–2
        Rest mass of 147N147N = 13.0942 GeVc–2 
        Rest mass of 178O+X178O+X = 16.8383 GeVc–2

The initial kinetic energy of the αα-particle is 7.68 MeV. Determine the sum of the kinetic energies of the oxygen nucleus and X. (Assume that the nitrogen nucleus is stationary.)

[4]
c.

The reaction in (c) produces oxygen (O-17). Other isotopes of oxygen include O-19 which is radioactive with a half-life of 30 s.

(i)  State what is meant by the term isotopes.

(i)  Define the term radioactive half-life.

 

[2]
d.

A nucleus of the isotope O-19 decays to a stable nucleus of fluorine. The half-life of O-19 is 30 s. At time t=0, a sample of O-19 contains a large number N0 nuclei of O-19.

On the grid below, draw a graph to show the variation with time t of the number N of O-19 nuclei remaining in the sample. You should consider a time of t=0 to t=120s.

 

[2]
e.

Markscheme

1/12th mass of an atom of carbon-12/12C ;

a.

(254.1001×931.5 =)236.7(GeVc−2 ); (only accept answer in GeV c−2 )

b.

(i) proton / hydrogen nucleus / H+11H11H / 11p11p;

(ii) ∆m=(16.8383-[3.7428+13.0942]=)0.0013(GeVc−2);
energy required for reaction = 1.3 (MeV);
178O+X=(7.681.3=)6.4(6.38)MeV178O+X=(7.681.3=)6.4(6.38)MeV; (allow correct answer in any valid energy unit)

c.

(i) (nuclei of same element with) same proton number, different number of neutrons / OWTTE;

(ii) the time for the activity of a sample to reduce by half / time for the number of the radioactive nuclei to halve from original value;

d.

scale drawn on t axis; (allow 10 grid squares ≡ 30 s or 40 s)

smooth curve passes through N02N02 at 30s, N04N04 at 60s, N08N08 at 90s, N016N016 at 120s
(to within 1 square); (points not necessary)

e.

Examiners report

 
a.
 
b.
 
c.
 
d.
 
e.

Syllabus sections

Core » Topic 7: Atomic, nuclear and particle physics » 7.1 – Discrete energy and radioactivity
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