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Q.
If the atom $_{100} Fm ^{257}$ follows the Bohr model and the radius of $_{100} Fm ^{257}$ is $n$ times the Bohr radius, then find $n$.
Atoms
Solution:
According to Bohr's model, $r_{m}=\left(\frac{m^{2}}{Z}\right) \times r_{0}$
where $m=$ orbit number, $r_{0}=$ Bohr radius
For $_{100} Fm ^{257}, Z=100$
$ \therefore m=5$
$\therefore r_{m}=\frac{(5)^{2}}{100} r_{0}$
According to given problem
$n r_{0}=\frac{(5)^{2}}{100} r_{0}$ or $n=\frac{1}{4}$