The nucleus of an atom can be assumed to be spherical. The radius… - Vidyadip

MCQ

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 ${\mathop A\limits^o }$. If the mass number is $64$, then the fraction of the atomic volume that is occupied by the nucleus is

A
$1.0 \times {10^{ - 3}}$
B
$5.0 \times {10^{ - 5}}$
C
$2.5 \times {10^{ - 2}}$
✓
$1.25 \times {10^{ - 13}}$

✓

Answer

Correct option: D.

$1.25 \times {10^{ - 13}}$

d
(d) 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\,\mathop A\limits^o $ $= {10^{ - 8}}\,cm.$

$\frac{{{\rm{Volume of nucleus}}}}{{{\rm{Volume of atom}}}}$$ = \frac{{(4/3)\pi \,{{(5 \times {{10}^{ - 13}})}^3}}}{{(4/3)\pi \,{{({{10}^{ - 8}})}^3}}}$

$ = 1.25\, \times {10^{ - 13}}$.

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