Solved: PHYSICS Question for NEET

NEET PHYSICSEasy

If the nuclear radius of ${}^{27}\mathrm{Al}$ is 3.6 Fermi, the approximate nuclear radius of ${}^{64}\mathrm{Cu}$ in Fermi is:

2.4

1.2

4.8

3.6

Formula: The nuclear radius $R$ is related to the mass number $A$ by the formula $R = R_0 A^{1/3}$ , where $R_0$ is a constant .
Identify Values:

Calculation: Taking the ratio of the radii: $\frac{R_{Cu}}{R_{Al}} = \left( \frac{A_{Cu}}{A_{Al}} \right)^{1/3}$ $\frac{R_{Cu}}{3.6} = \left( \frac{64}{27} \right)^{1/3}$ $\frac{R_{Cu}}{3.6} = \frac{(4^3)^{1/3}}{(3^3)^{1/3}} = \frac{4}{3}$ $R_{Cu} = 3.6 \times \frac{4}{3} = 1.2 \times 4 = 4.8 \text{ Fermi}$

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