Nuclei - Result Question 5

5. The radius of germanium $(Ge)$ nuclide is measured to be twice the radius of $ _4^{9} Be$. The number of nucleons in Ge are

[2006]

(a) 74

(b) 75

(c) 72

(d) 73

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Answer:

Correct Answer: 5. (c)

Solution:

  1. (c) We use the formula,

$R=R_0 A^{1 / 3}$

This represents relation between atomic mass and radius of the nucleus.

For berillium,

For germanium, $\quad R_2=R_0 A^{1 / 3}$

$\frac{R_1}{R_2}=\frac{(9)^{1 / 3}}{(A)^{1 / 3}} \Rightarrow \frac{1}{2}=\frac{(9)^{1 / 3}}{(A)^{1 / 3}}$

$\Rightarrow \frac{1}{8}=\frac{9}{A} \Rightarrow A=8 \times 9=72$.