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### Fundamentals Of Physics

Book edition 10th Edition
Author(s) David Halliday
Pages 1328 pages
ISBN 9781118230718

# Figure 40-21 shows partial energy-level diagrams for the helium and neon atoms that are involved in the operation of a helium–neon laser. It is said that a helium atom in state ${{\mathbit{E}}}_{{\mathbf{3}}}$ can collide with a neon atom in its ground state and raise the neon atom to state ${{\mathbit{E}}}_{{\mathbf{2}}}$. The energy of helium state ${{\mathbit{E}}}_{{\mathbf{3}}}\left(20.61eV\right)$is close to, but not exactly equal to, the energy of neon state role="math" localid="1661494292758" ${{\mathbit{E}}}_{{\mathbf{2}}}\mathbf{\left(}\mathbf{20}\mathbf{.}\mathbf{66}\mathbf{}\mathbf{eV}\mathbf{\right)}$. How can the energy transfer take place if these energies are not exactly equal?

The energy transfer takes place due to the excitation caused by the current in the helium atoms by collisions (not the more massive neon atoms).

See the step by step solution

## Step 1: The given data

1. Figure 40-21 show partial energy-level diagrams for the helium and neon atoms that are involved in the operation of the helium-neon laser is given.
2. The energy of the helium state ${E}_{3}\left(20.61\mathrm{eV}\right)$ is very close to the energy of the neon state ${E}_{3}\left(20.66\mathrm{eV}\right)$.

## Step 2: Understanding the concept of laser action

Due to the laser action, there occurs a potential difference that gives rise to the current passing through the helium-neon gas mixture serving—through collisions between helium atoms and electrons of the current—to raise many helium atoms to state E3, which is metastable with a mean life of 1 microsec. (The neon atoms are too massive to be excited by collisions with the (low-mass) electrons.)

## Step 3: Calculation of the reason for energy transfer

According to the given data and concept, when a metastable $\left({E}_{3}\right)$ helium atom and a ground state $\left({E}_{0}\right)$ neon atom collide, the excitation energy of the helium atom is often transferred to the neon atom, which then moves to the state ${E}_{2}$ . In this manner, neon level ${E}_{2}$ (with a mean life of 170 ns) can become more heavily populated than neon level role="math" localid="1661494432656" ${E}_{1}$ (which, with a mean life of only 10 ns, is almost empty).

This population inversion is relatively easy to set up because (1) initially, there are essentially no neon atoms in the state ${E}_{1}$, and (2) the long mean life of helium level ${E}_{3}$ means that there is always a good chance that collisions will excite neon atoms to their level, ${E}_{2}$ and (3) once those neon atoms undergo stimulated emission and fall to their ${E}_{1}$ level, they almost immediately fall down to their ground state (via intermediate levels not shown) and are then ready to be re-excited by collisions.

Hence, the energy transfer occurs even if the energy levels of helium and neon are not the same.