Calculate the radius of the $n = 4$ Bohr orbit in $\mathrm { O } ^ { 7 + }$ (oxygen with 7 of its 8 electrons removed). (for hydrogen, $r _ { 1 } = 0.0529 \mathrm {~nm}$ )
A) $85 \mathrm { pm }$
B) $95 \mathrm { pm }$
C) $74 \mathrm { pm }$
D) $106 \mathrm { pm }$

Question

Quizplus · Accepted Answer

The radius of the $n^{th}$ Bohr orbit for a hydrogen-like atom is given by $r_n = n^2 \times \frac{r_1}{Z}$, where $r_1$ is the radius of the first Bohr orbit for hydrogen, $n$ is the principal quantum number, and $Z$ is the atomic number of the ion. For $O^{7+}$, $Z = 8$, and for the $n = 4$ orbit, the formula becomes $r_4 = 4^2 \times \frac{0.0529 \, \text{nm}}{8} = 0.106 \, \text{nm} = 106 \, \text{pm}$.

Calculate the Radius of The n=4n = 4n=4 Bohr Orbit In O7+\mathrm { O } ^ { 7 + }O7+

Calculate the Radius of The $n = 4$ Bohr Orbit In $\mathrm { O } ^ { 7 + }$