Question

The mean momentum of a nucleon inside a nucleus with mass number $A$ varies as

• A. $A^{3}$
• B. $A^{- \frac{2}{3}}$
• C. $A^{- \frac{1}{3}}$
• D. $A^{\frac{1}{3}}$
• E. $A^{\frac{2}{3}}$

Answer 1

Answer: (C)

From the Heisenberg uncertainty principle, $\Delta p\geq \frac{h}{4 \pi \Delta r}$ $p\lambda =constant.$
$p∝​\frac{1}{\lambda }\approx\frac{1}{r}\approx\frac{1}{A^{\frac{1}{3}}}$