- #1
hetanshu
- 2
- 0
why do electrons revolve around the nucleus?
so are they stationary?
Not true in general. You can see this by calculating the expectation value of the momentum of the electron from its wavefunction, and finding that the momentum is in general nonzero.Electrons are stationary wave
They are not noving
Electrons are stationary wave
They are not noving
Thank you for the clarification.The expectation value of the momentum [itex]\langle p \rangle[/itex] of an electron in a single orbital [itex](n, \ell, m_{\ell})[/itex] is indeed zero. This can be seen from Ehrenfest's theorem, and that the expectation value of the position is a constant for one of these eigenstates.
However, the variance of the momentum [itex]\sigma_{p}^{2}[/itex] is nonzero even in these states, which means that you are very likely to find the electron having a nonzero momentum if you actually measure it (it's only zero "on average").
Also, most electrons (I would think) exist in a superposition of different orbitals (i.e., their wavefunctions are not stationary, even if they are still concentrated around the nucleus). In this case, the expectation value of the momentum may change in time all sorts of ways.
i will checkNot true in general. You can see this by calculating the expectation value of the momentum of the electron from its wavefunction, and finding that the momentum is in general nonzero.
This may be nitpicking, but even in eigenstates [itex]\langle p \rangle[/itex] is only zero in one inertial frame---the one in which the nuclear core to which the electron belongs is at rest. If the entire atom is moving (core and all), the electrons have non-zero expectation values of momentum, too.The expectation value of the momentum [itex]\langle p \rangle[/itex] of an electron in a single orbital [itex](n, \ell, m_{\ell})[/itex] is indeed zero. This can be seen from Ehrenfest's theorem, and that the expectation value of the position is a constant for one of these eigenstates.