Mean value of momentum of electron in H atom

In summary, the mean value of momentum of an electron in a hydrogen atom is related to its energy and is affected by changes in the atom's energy levels. It cannot be negative and may change over time, but is a conserved quantity. It is given by the equation p = nh/λ and is directly related to energy through the equation E = (p^2 / 2m) - (ke^2 / r).
  • #1
superyoon
1
0

Homework Statement


What is the mean value of the momentum of an electron of a hydrogen atom in its ground state? Derive this mean value of the momentum from the kinetic energy of the electron.


Homework Equations


<p> = integral from -infinity to infinity (p*|psi|^2) dx
p^2/2m = KE



The Attempt at a Solution


I solved the equation above for p; p = sqrt(2m*KE). <p> = integral from -infinity to infinity [sqrt(2m*KE)*|psi|^2]dx, but I don't know where to go from here.

Thanks.
 
Physics news on Phys.org

FAQ: Mean value of momentum of electron in H atom

What is the mean value of momentum of an electron in a hydrogen atom?

The mean value of momentum of an electron in a hydrogen atom is given by the equation p = nh/λ, where n is the principle quantum number, h is Planck's constant, and λ is the wavelength.

How is the mean value of momentum of an electron in a hydrogen atom related to its energy?

The mean value of momentum of an electron in a hydrogen atom is directly related to its energy through the equation E = (p^2 / 2m) - (ke^2 / r), where m is the mass of the electron, ke is Coulomb's constant, and r is the distance between the electron and the nucleus.

Can the mean value of momentum of an electron in a hydrogen atom be negative?

No, the mean value of momentum of an electron in a hydrogen atom cannot be negative. It is a vector quantity with direction, but its magnitude is always positive.

How is the mean value of momentum of an electron in a hydrogen atom affected by changes in the atom's energy levels?

The mean value of momentum of an electron in a hydrogen atom changes with the energy levels of the atom. As the electron moves to a higher energy level, its momentum increases, and as it moves to a lower energy level, its momentum decreases.

Is the mean value of momentum of an electron in a hydrogen atom constant over time?

No, the mean value of momentum of an electron in a hydrogen atom can change over time as the electron moves and interacts with other particles. However, it is a conserved quantity, meaning that the total momentum of the electron will remain constant in a closed system.

Similar threads

Expectation value <p> of the ground state of hydrogen
Replies
4
Views
4K
What happens to an atom's angular momentum when it absorbs an electron?
Replies
1
Views
2K
Quantum Virial Theorem Derivation
Replies
10
Views
2K
Time evolution of a particle in momentum space
Replies
1
Views
2K
Time Independence of the Momentum Uncertainty for a Free Particle Wave
Replies
3
Views
2K
Difference between average position of electron and average separation
Replies
14
Views
2K
Proton in a 1D Box: Energy, Probability, Speed
Replies
24
Views
2K
Bohr-Sommerfeld, WKB, and current-biased Josephson junction
Replies
1
Views
1K
Use the uncertainty principle for momentum vs. position to e
Replies
2
Views
1K
Continuity Equation for a Dimensionless Harmonic Oscillator
Replies
16
Views
1K

Hot Threads

Recent Insights

Back
Top