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GATE 2020 PH – Question 46

Nuclear and Particle Physics · Nuclear models · 2 marks · Multiple choice

In the nuclear Fermi-gas model, nucleons occupy a sphere of radius $R=R_0A^{1/3}$, where A is mass number. The Fermi energy scales with $R_0$ as

  1. $R_0^2$
  2. $R_0^{-1}$
  3. $R_0^{-2}$
  4. $R_0^{-3}$

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Correct answer: (C) $R_0^{-2}$

Explanation

Number density is proportional to $A/R^3=A/(R_0^3A)\propto R_0^{-3}$. Fermi momentum scales as $p_F\propto n^{1/3}\propto R_0^{-1}$. In the nonrelativistic nuclear Fermi-gas model, $E_F=p_F^2/(2m)$, hence $E_F\propto R_0^{-2}$. Select C.