Why is the kinetic energy of an electron in a hydrogen atom at $n=2$ level, the negative of its total energy?

Question

My textbook [1] says in order to determine the De Broglie wavelength of an $e^-$ in a hydrogen atom at energy level $n=2$, we can determine its kinetic energy first by finding its total energy from $E=-13.6/n^2$ then determine its De Broglie wavelength accordingly.

But isn't the total energy of the electron at $n=2$ refers to its potential and kinetic energy? How can we simply take the negative of the electron's total energy and call it the electron KE? This implies that at $n=\infty$ then electron's KE is 0; vice versa when $n=0$ then electron's KE is $\infty$.

References:

K. A. Tsokos, "Physics for the IB Diploma Coursebook" 6th Edition

Note that $n = 1, 2, 3, \cdots$. It does not include zero. – K_inverse Oct 19 '18 at 05:42 — K_inverse, Oct 19 '18 at 05:42

score 1 · Answer 1 · answered Oct 19 '18 at 10:21

1

Hints:

Note that the principal quantum number $n\in\mathbb{N}$ cannot be zero.
Use the virial theorem. See also this related Phys.SE post.

answered Oct 19 '18 at 10:21

Qmechanic

201,751

But virial theorem has to do with the system not with the electron. So how can be used? – Antonios Sarikas Feb 13 '20 at 17:19
The 2-body system (electron + nucleus) is reduced to a 1-body system because we work in the center-of-mass reference frame. – Qmechanic Feb 13 '20 at 17:33
What if we work with multi-electron atoms? Would we neglect the motion of nucleus? – Antonios Sarikas Feb 23 '20 at 12:59
Ideally, we should not neglect the motion of the nucleus in the center-of-mass reference frame. – Qmechanic Feb 23 '20 at 13:06

score -1 · Answer 2 · answered Oct 19 '18 at 05:42

-1

It's a formalism from harmonic oscillator, so that when electron come from $n=2$ to $n=1$, it releases energy.

Also, without nature presetance of fields or confirment, $H$ can be ionized if you insist, there are just so many quantized value that one could take. Calling it KE is from hamiltonian operator. It's a correspondance with classical physcis.

answered Oct 19 '18 at 05:42

ShoutOutAndCalculate

3,224

What does "nature presetance of fields or confirment" mean? – PM 2Ring Feb 07 '19 at 07:13

Why is the kinetic energy of an electron in a hydrogen atom at $n=2$ level, the negative of its total energy?

2 Answers2