Question

If the atom $_{100} Fm ^{257}$ follows the Bohr's model and the radius of $_{100} Fm ^{257}$ is $n$ times the Bohr radius, then find $n$ :

• A. 100
• B. 200
• C. 4
• D. $ \frac{1}{4} $

Answer 1

Answer: (D)

$r_{m}=\left(\frac{m^{2}}{z}\right)(0.53 \,\mathring{A}) $
$=(r \times 0.53\,\mathring{A})$
$\therefore \frac{m^{2}}{z}=n$
Here $m=5$ for $_{100} F m^{257}$
(the outermost shell) and $z=100$
$\therefore n=\frac{(5)^{2}}{100}=\frac{1}{4}$