Calculate the ratio of the velocity of an electron in the Bohr orbit of a hydrogen atom to that in t — Atomic Structure Chemistry Question

💡 Solution & Explanation

The velocity of an electron in a Bohr orbit is given by $v \propto \frac{Z}{n}$. For the $1^{st}$ orbit of H ($Z=1, n=1$), $v_H \propto \frac{1}{1} = 1$. For the $3^{rd}$ orbit of $Be^{3+}$ ($Z=4, n=3$), $v_{Be} \propto \frac{4}{3}$. The ratio is $\frac{v_H}{v_{Be}} = \frac{1}{4/3} = \frac{3}{4}$. Here, $x=3$ and $y=4$, so $x+y = 3+4=7$.