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# The order of size of nucleus and Bohr radius of an atom respectively are:A. ${10^{ - 14}}m,{10^{ - 10}}m$B. ${10^{ - 10}}m,{10^{ - 8}}m$C. ${10^{ - 20}}m,{10^{ - 16}}m$D. ${10^{ - 8}}m,{10^{ - 6}}m$

Last updated date: 12th Aug 2024
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Hint: We know that the density of any nucleus is constant. So the volume of the nucleus will be proportional to the mass number of the nucleus. From the volume we can get the radius of the nucleus. According to Bohr, there is a formula to find out the radius of Bohr's orbit and this is only applicable for hydrogen like species.

Formula used:
$R = 0.53 \times \dfrac{{{n^2}}}{Z}{A^ \circ }$

$R = 0.53 \times \dfrac{{{n^2}}}{Z}{A^ \circ }$
Where ‘n’ is the principal quantum number and Z is the atomic number. Above radius is measured in angstroms. That means order of ${10^{ - 10}}m$.
Now coming to the radius of the nucleus, it will be proportional to mass number. But whatever may be the mass number, only value changes but order will remain the same. It will be of order ${10^{ - 14}}m$.