Question

If the radii of ${}_{13}^{27}Al$ and ${}_{30}^{64}Zn$ nucleus are $R_1$ & $R_2$ respectively, then $\frac{R_1}{R_2}=$ ____________.

• A. $\frac{27}{64}$
• B. $\frac{3}{4}$
• C. $\frac{9}{16}$
• D. $\frac{13}{30}$

Answer 1

The correct option is B $\frac{3}{4}$

The relation between the Atomic weighr (A) and nucleu radius(R) is given by $R=R_0{A}^{\frac{1}{3}}$

Here, $R_1=R_0{A}_1^{\frac{1}{3}}$

$\Rightarrow$ $R_1=3R_0$ $(\because A_1=27)$ ...$eq.1$

Using this relation again,

$R_2=R_0{A}_2^{\frac{1}{3}}$

$\Rightarrow$ $R_2=4R_0$ $(\because A_2=64)$ ...$eq.1$

Now,on dividing both equation, we get

$\frac{R_1}{R_2}=\frac{3}{4}$

Therefore option B is correct.