The radius of germanium $(\mathrm{Ge})$ nuclide is measured to be twice the radius of ${ }_4^9 \mathrm{Be}$.…

The radius of germanium $(\mathrm{Ge})$ nuclide is measured to be twice the radius of ${ }_4^9 \mathrm{Be}$. The number of nucleons in Ge will be
  1. $72$
  2. $73$
  3. $74$
  4. $75$

Solution

Using radius of a nucleus, $\mathrm{R} \propto \mathrm{A}^{1 / 3}$ Where, $A=$ number of nucleons $\begin{aligned} & \therefore \quad \frac{R_{G e}}{R_{B e}}=\left(\frac{A_{G e}}{A_{B e}}\right)^{1 / 3} \\ & 2=\left(\frac{A_{G e}}{A_{B e}}\right)^{1 / 3} \text { or, } 2^3=\frac{A_{G e}}{A_{B e}} \quad\left(\therefore R_{G e}=2 R_{B e}\right) \\ & 2^3=\frac{A_{G e}}{9} \quad\left[\therefore A_{B e}=9\right] \\ & \therefore \quad A_{G e}=2^3 \times 9=8 \times 9=72 \end{aligned}$

Asked in: AP EAMCET 2016

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