Modern Physics 1 Question 20
17. If the atom ${ } _{100} Fm^{257}$ follows the Bohr’s model and the radius of last orbit of ${ } _{100} Fm^{257}$ is $n$ times the Bohr radius, then find $n$
$(2003,2 M)$
(a) 100
(b) 200
(c) 4
(d) $1 / 4$
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Solution:
- $\quad\left(r _m\right)=\frac{m^{2}}{z}(0.53 \AA)=(n \times 0.53) \AA$
$$ \therefore \quad \frac{m^{2}}{z}=n $$
$m=5$ for ${ } _{100} Fm^{257}$ (the outermost shell) and $z=100$
$$ \therefore \quad n=\frac{(5)^{2}}{100}=\frac{1}{4} $$
