A) the helium nucleus has more kinetic energy than the thorium nucleus
B) the helium nucleus has less momentum than the thorium nucleus
C) the helium nucleus has more momentum than the thorium nucleus
D) the helium nucleus has less kinetic energy than the thorium nucleus
Correct Answer: A
Solution :
| \[_{92}{{U}^{238}}{{\xrightarrow{\,}}_{92}}T{{h}^{238}}{{+}_{2}}H{{e}^{4}}\] |
| According to law of conservation of linear momentum, we have. |
| \[\left| {{\mathbf{P}}_{\text{Th}}} \right|=\left| {{\mathbf{P}}_{\text{He}}} \right|=\mathbf{P}\] |
| \[\Rightarrow \] As, kinetic energy of an element, |
| \[KE=\frac{{{P}^{2}}}{2m}\] |
| where, m is mass of an element. |
| Thus, \[KE\propto \frac{1}{M}\] |
| So, \[{{M}_{He}}<{{M}_{Th}}\Rightarrow {{K}_{He}}>{{K}_{Th}}\] |
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