Question

Do the planets of the solar system obey a distance law${\mathit{r}}_{\mathbf{n}}\mathbf{=}{\mathit{n}}^{\mathbf{2}}{\mathit{r}}_{\mathbf{1}}$ as the electrons of the Bohr atom do? Should they? Why (or why not)? (Consult Appendix F for the appropriate distances).

Short answer

Planets of solar system don’t obey distance law$r_n=n^2{r}_1$ as the electrons of the Bohr atom. They should not because momentum of solar system is continuous.

Step-by-step solution

Explain distance law

Distance law states that radius of nth body revolving around a heavy mass is n square times of radius of first body revolving around the same mass.

$r_n=n^2{r}_1$

This law is only applicable to those revolving bodies who have quantized momentum.

Apply distance law to electrons and planets

In solar system, revolving body is planets and the heavy mass is sum while in atom, revolving body is electrons and the heavy mass is nucleus.

Being in same type of motion still planets don’t follow distance law while electrons do. This is because electrons show wave nature which leads to their momentum quantized condition. And planets being large masses, don’t exhibit dominant wave nature and behave like particle which results in their momentum is continuous.

The basic requirement of distance law is momentum quantization. This only electrons can fulfill and obey distance law.

Hence, Planets of solar system don’t obey distance law$r_n=n^2{r}_1$ as the electrons of the Bohr atom. They should not because momentum of solar system is continuous.