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# As the Earth moves around the Sun, its orbits are quantized. (a) Follow the steps of Bohr’s analysis of the hydrogen atom to show that the allowed radii of the Earth’s orbit are given by $$r_{n}=\frac{n^{2} \hbar^{2}}{G M_{S} M_{E}^{2}}$$where $n$ is an integer quantum number, $M_{S}$ is the mass of the Sun, and $M_{E}$ is the mass of the Earth. (b) Calculate the numerical value of $n$ for the Sun-Earth system. (c) Find the distance between the orbit for quantum number $n$ and the next orbit out from the Sun corresponding to the quantum number $n+1 .$ (d) Discuss the significance of your results from parts (b) and (c).

## a) $r_{n}=\frac{n^{2} \hbar^{2}}{G M_{S} M_{E}^{2}}$b) $2.54 \times 10^{74}$c) $1.18 \times 10^{-6.3} \mathrm{m}$d) answer not available

Atomic Physics

Nuclear Physics

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##### Christina K.

Rutgers, The State University of New Jersey

LB
##### Jared E.

University of Winnipeg

### Video Transcript

Universidade de Sao Paulo

#### Topics

Atomic Physics

Nuclear Physics

##### Christina K.

Rutgers, The State University of New Jersey

LB
##### Jared E.

University of Winnipeg