Sodium-22 decays by positron emission according to ^ 22 _ 11 Na ; ;^ 22 _ 10 Ne +e^ +…

PHYSICS · Multi-part · A Level · Physics · Nuclear physics · Nuclear physics

Problem

Sodium-22 decays by positron emission according to

^{22}_{11}\mathrm{Na}\;\rightarrow\;^{22}_{10}\mathrm{Ne}+e^{+}+\nu_{e}+\gamma,

where a

\gamma

-ray of energy

1.274\,\text{MeV}

is emitted. The atomic masses are:

^{22}_{11}\mathrm{Na}=21.994436\,\text{u}

^{22}_{10}\mathrm{Ne}=21.991385\,\text{u}

. The rest mass of the positron is

0.00054858\,\text{u}

. Assume the neutrino carries away

0.300\,\text{MeV}

of kinetic energy. Use

1\,\text{u}=931.5\,\text{MeV}

. (i) Calculate the

Q

-value (energy release) for the decay in MeV. (ii) Deduce the kinetic energy acquired by the positron, assuming the recoil energy of the neon nucleus is negligible. (iii) State whether the decay is endothermic or exothermic and justify your answer using the sign of the

Q

-value.

Related theory

Mass-Energy Equivalence
Radioactivity
Nuclear physics
Atomic Structure
Nuclei

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