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Date November 2015 Marks available 2 Reference code 15N.3.SL.TZ0.7
Level Standard level Paper Paper 3 Time zone Time zone 0
Command term Explain Question number 7 Adapted from N/A

Question

This question is about radioactive decay.

Meteorites contain a small proportion of radioactive aluminium-26 \(\left( {_{{\text{13}}}^{{\text{26}}}{\text{Al}}} \right)\) in the rock.

The amount of \(_{{\text{13}}}^{{\text{26}}}{\text{Al}}\) is constant while the meteorite is in space due to bombardment with cosmic rays.

After reaching Earth, the number of radioactive decays per unit time in a meteorite sample begins to diminish with time. The half-life of aluminium-26 is \(7.2 \times {10^5}\) years.

Aluminium-26 decays into an isotope of magnesium (Mg) by \({\beta ^ + }\) decay.

\[_{{\text{13}}}^{{\text{26}}}{\text{Al}} \to _{\text{Y}}^{\text{X}}{\text{Mg}} + {\beta ^ + } + {\text{Z}}\]

Identify X, Y and Z in this nuclear decay process.

 

X:

Y:

Z:

[2]
a.

Explain why the beta particles emitted from the aluminium-26 have a continuous range of energies.

[2]
b.

State what is meant by half-life.

[1]
c.i.

A meteorite which has just fallen to Earth has an activity of 36.8 Bq. A second meteorite of the same mass, which arrived some time ago, has an activity of 11.2 Bq. Determine, in years, the time since the second meteorite arrived on Earth.

[3]
c.ii.

Markscheme

X: 26 and Y: 12; (both needed for [1])

Z: v/neutrino;

Do not allow the antineutrino.

a.

total energy released is fixed;

neutrino carries some of this energy;

(leaving the beta particle with a range of energies)

b.

the time taken for half the radioactive nuclides to decay / the time taken for the activity to decrease to half its initial value;

Do not allow reference to change in weight.

c.i.

\(\lambda  = \left( {\frac{{\ln 2}}{{7.2 \times {{10}^5}}} = } \right){\text{ }}9.63 \times {10^{ - 7}}\);

\(11.2 = 36.8{e^{ - (9.63 \times {{10}^{ - 7}})t}}\);

\(t = 1.24 \times {10^6}{\text{ (yr)}}\);

c.ii.

Examiners report

This was generally well answered, although a significant minority insisted that nuclear half-life is defined by a loss of mass.

a.

This was generally well answered, although a significant minority insisted that nuclear half-life is defined by a loss of mass.

b.

This was generally well answered, although a significant minority insisted that nuclear half-life is defined by a loss of mass.

c.i.

This was generally well answered, although a significant minority insisted that nuclear half-life is defined by a loss of mass.

c.ii.

Syllabus sections

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