Calculate the orbital Bohr radius of the $n = 2$ excited state in a hydrogen atom. $\left( r _ { 1 } = 0.0529 \mathrm {~nm} \right)$
A) $0.212 \mathrm {~nm}$
B) $0.170 \mathrm {~nm}$
C) $0.106 \mathrm {~nm}$
D) $0.244 \mathrm {~nm}$

Question

Quizplus · Accepted Answer

The Bohr radius for an electron in the $n$th energy level of a hydrogen atom is given by $r_n = n^2 r_1$, where $r_1$ is the Bohr radius for the ground state ($n=1$). Given $r_1 = 0.0529 \mathrm{~nm}$ and $n=2$, $r_2 = 2^2 \times 0.0529 \mathrm{~nm} = 0.2116 \mathrm{~nm}$, which rounds to $0.212 \mathrm{~nm}$.

Calculate the Orbital Bohr Radius of The n=2n = 2n=2 Excited State in a Hydrogen Atom

Calculate the Orbital Bohr Radius of The $n = 2$ Excited State in a Hydrogen Atom