Atomic Structure Question 121
Question: The nucleus of an atom can be assumed to be spherical. The radius of the nucleus of mass number $ A $ is given by $ 1.25\times {10^{-13}}\times {A^{1/3}}cm $ Radius of atom is one $ {\AA} $ . If the mass number is 64, then the fraction of the atomic volume that is occupied by the nucleus is [NCERT 1983]
Options:
A) $ 1.0\times {10^{-3}} $
B) $ 5.0\times {10^{-5}} $
C) $ 2.5\times {10^{-2}} $
D) $ 1.25\times {10^{-13}} $
Show Answer
Answer:
Correct Answer: D
Solution:
Radius of nucleus $ =1.25,\times {10^{-13}}\times {A^{1/3}},cm $
$ =1.25,\times {10^{-13}}\times {64^{1/3}} $
$ =5\times {10^{-13}},cm $ Radius of atom = $ 1\text{{ }AA},={10^{-8}}cm. $
$ \frac{\text{Volume of nucleus}}{\text{Volume of atom}} $
$ =\frac{(4/3)\pi ,{{(5\times {10^{-13}})}^{3}}}{(4/3)\pi ,{{({10^{-8}})}^{3}}} $
$ =1.25,\times {10^{-13}} $ .
