Atoms And Nuclei Question 331
Question: The nuclear radius of a nucleus with nucleon number 16 is $ 3\times {{10}^{-15}}m $ . Then, the nuclear radius of a nucleus with nucleon number 128 is
Options:
A) $ 3\times {{10}^{-15}}m $
B) $ 1.5\times {{10}^{-15}}m $
C) $ 6\times {{10}^{-15}}m $
D) $ 4.5\times {{10}^{-15}}m $
Show Answer
Answer:
Correct Answer: C
Solution:
- Radius R os a nucleus changes with the nucleon number A of the nucleus as
$ R=1.3\times {{10}^{-15}}\times {{A}^{1/3}}m $
Hence, $ \frac{R_{2}}{R_{1}}={{( \frac{A_{2}}{A_{1}} )}^{1/3}}={{( \frac{128}{16} )}^{1/3}}={{(8)}^{1/3}}=2 $
$ \therefore R_{2}=2R_{1}=2(3\times {{10}^{-15}})m=6\times {{10}^{-15}}m $
