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Q. Assume that the radius of the first Bohr orbit of hydrogen atom is $0.6 \mathring{A}$. The radius of the third Bohr orbit of $He ^{+}$ is ___ picometer. (Nearest Integer)

JEE MainJEE Main 2023Structure of Atom

Solution:

$ r \propto \frac{ n ^2}{ Z }$
$ r _{ He ^{+}} = r _{ H } \times \frac{ n ^2}{ Z } $
$ r _{ He ^{+}} =0.6 \times \frac{(3)^2}{2} $
$ =2.7 \mathring{A} $
$r _{ He ^{+}} =270 \,pm$