Physics

Problem

\alpha

-decay process is represented schematically as

^{238}_{\ 92}\text{U} \;\rightarrow\; ^{234}_{\ 90}\text{Th} + ^{4}_{\ 2}\text{He}.

The following nuclear masses are given:

^{238}_{\ 92}\text{U}: 238.050788\,\text{u}

^{234}_{\ 90}\text{Th}: 234.043593\,\text{u}

^{4}_{\ 2}\text{He}: 4.002603\,\text{u}

. (Atomic-electron masses are already included in these tabulated values.) a. (a) Write the numerical value of the total mass of the decay products and hence find the mass defect

\Delta M

for the decay. b. (b) Calculate the energy (in MeV) released in this

\alpha

-decay. Use

1\,\text{u}=931\,\text{MeV}

. c. (c) Briefly state how this released energy is shared between the emitted

\alpha

-particle and the recoiling thorium nucleus.

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