# Mean value of momentum of electron in H atom

• superyoon
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).
superyoon

## 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.

## 1. 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.

## 2. 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.

## 3. 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.

## 4. 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.

## 5. 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.

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