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Question: If the nucleus of \(13Al^{27}\) has a nuclear radius of about \(3.6\) fm then \(52Te^{125}\) would h...

If the nucleus of 13Al2713Al^{27} has a nuclear radius of about 3.63.6 fm then 52Te12552Te^{125} would have its radius approximately as

A

9.6fm9.6fm

B

12 fm

C

4.8fm4.8fm

D

6 fm

Answer

6 fm

Explanation

Solution

: Here, A1=27,A2=125A_{1} = 27,A_{2} = 125

R1=3.6fmR_{1} = 3.6fm

As R2R1=(A2A1)1/3=(12527)1/3=53\frac{R_{2}}{R_{1}} = \left( \frac{A_{2}}{A_{1}} \right)^{1/3} = \left( \frac{125}{27} \right)^{1/3} = \frac{5}{3}

R2=53R1=53×3.6=6fm\therefore R_{2} = \frac{5}{3}R_{1} = \frac{5}{3} \times 3.6 = 6fm