Radium-226 undergoes -decay according to ^ 226 _ 88 Ra ,^ 222 _ 86 Rn + ,^ 4 _ 2 He…

PHYSICS · Subjective · A Level · Physics · Nuclear physics · Nuclear physics

Problem

Radium-226 undergoes

\alpha

-decay according to

^{226}_{88}\text{Ra}\rightarrow\,^{222}_{86}\text{Rn}+\,^{4}_{2}\text{He}

Given the following nuclear masses: •

^{226}\!\text{Ra}=226.025\,40\,\text{u}

•

^{222}\!\text{Rn}=222.017\,57\,\text{u}

•

^{4}\!\text{He}=4.002\,60\,\text{u}

Constants: mass of proton

=1.007\,276\,\text{u}

, mass of neutron

=1.008\,665\,\text{u}

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

. (i) Determine the binding energy per nucleon of the parent

^{226}\!\text{Ra}

nucleus. (ii) Calculate the binding energy per nucleon of the daughter

^{222}\!\text{Rn}

nucleus. (iii) Compute the energy released (in MeV) in a single

\alpha

-decay of

^{226}\!\text{Ra}

. (iv) Comment on how the values obtained in parts (i) and (ii) support the possibility of this decay process.