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  4. If the atom 100Fm257 follows the Bohr's model and the radius of last orbit of 100Fm257 is n times the Bohr radius, then find n

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Q. 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

IIT JEEIIT JEE 2003

Solution:

$(r_m)=\bigg(\frac{m^2}{Z}\bigg)(0.53\mathring{A})$
$=(n\times0.53)\mathring{A}$
$\therefore \frac{m^2}{Z}=n$
m = 5 for $_{100}Fm^{257}$ (the outermost shell) and z = 100
$\therefore n=\frac{(5)^2}{100}=\frac{1}{4}$