Chapter 36, Problem 1FTD

To determine

what plays the role of confining box in a hydrogen atom.

Answer to Problem 1FTD

Quantum numbers associated with the atom plays the role of confinement box.

Explanation of Solution

Particle in a box is a quantum mechanical treatment for finding the energy levels of atoms and molecules or general systems. Hydrogen is the simplest atom that we can study. And the results associated with hydrogen would help us find the results for other hydrogen like atoms.

Here we have to find the entity that acts as the confining box if we consider hydrogen atom to be confined in a box. When we solve the Schrodinger equations of this hydrogen atom we get the various quantum numbers that make the angular momentum and energy of the system quantified.

Write the equation to get the orbital angular momentum.

$L=\sqrt{l\left(l+1\right)}\hslash$

Here,

$L$ is the angular momentum

$l$ is the angular momentum of the atom.

Thus we can see that the angular momentum of the atom is an integral multiple of $\hslash$ and thus it is quantified or confined. Therefore the quantum numbers that we get from solving Schrodinger equation plays the role of confining box.

Conclusion:

Quantum numbers associated with the atom plays the role of confinement box.