- #1

fluidistic

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## Homework Statement

According to Bohr's atomic model,

1)Determine the allowed radius of the orbit of the electrons. Calculate the radius of the first orbit for the hydrogen atom.

2)Show that the energy of the electron is quantized. Calculate the energy corresponding to an electron on the first Bohr's orbit in an atom of H.

3)Justify the use of classical mechanics instead of relativistic mechanics for light atoms.

4)Redo part 1 and 2 assuming that the nucleous' mass isn't infinite.

## Homework Equations

Somes.

## The Attempt at a Solution

1)I erroneously considered only the H atom. I started by equating coulomb's force to centripetal force. Then writing down the kinetic and potential energy of an electron in the atom.

Then I used the fact that the angular momentum is quantized (I've found this way in a book). Then using some arithmetics tricks, I reached that [tex]r=\frac{n^2 \hbar ^2}{e^2 k m_e}[/tex] where k is the constant in Coulomb's law (worth 1 in some unit system, etc.), [tex]n\in \mathbb{N}- \{ 0 \}[/tex], [tex]m_e[/tex] is the rest mass of the electron and [tex]e[/tex] is the electron charge.

So for the hydrogen atom, n=1, right?

If I'm not wrong and Z is the number of protons in the nucleus, I should have reached [tex]r=\frac{n^2 \hbar ^2}{e^2 k m_e Z}[/tex] is this right? And in this case, n=2 makes sense while in my first expression it wouldn't, am I right?

2)I reached [tex]E=\frac{e^4 k m_e}{n^2 \hbar} \left ( \frac{k^2e^2m_e}{2n^2 \hbar ^2} -1 \right)[/tex], is it right? If I set n=1 I answer the second question of part 2).

3)Should I calculate the velocity of an electron? I could just use the Coulomb's law equated to the centripetal force expression and get v taking a square root. Is this right?

4)Seems really hard.