Q137 / 160 · AP EAMCET 2014 · Physics

If the radius of a nucleus with mass number 125 is 1.5 fermi, then radius of a nucleus with mass number 64 is

  • A
    0.48 fermi
  • B
    0.96 fermi
  • C
    1.92 fermi
  • Correct answer
    D
    1.2 fermi

Solution

By Rutherford's experiment $\begin{aligned} R_1 & =R_0 A_1^{1 / 3} \\ R_2 & =R_0 A_2^{1 / 3} \end{aligned}$ Given $\begin{aligned} R_1 & =1.5 \text { fermi } \\ A_1 & =125 \\ A_2 & =64 \\ R_2 & =? \end{aligned}$ Now, $\frac{R_1}{R_2}=\left(\frac{A_1}{A_2}\right)^{1 / 3} \quad$ [from the Eqs. (i) and (ii)] $\begin{aligned} & \frac{1.5}{R_2}=\left(\frac{125}{64}\right)^{1 / 3} \\ & \Rightarrow \quad \frac{1.5}{R_2}=\frac{5}{4} \\ & \Rightarrow \quad R_2=\frac{1.5 \times 4}{5}=0.3 \times 4 \\ & =1.2 \text { fermi } \end{aligned}$

Hence, the correct answer is option: 'D'.

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