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Q.(26)

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Found in: Page 1114

### Physics for Scientists and Engineers: A Strategic Approach with Modern Physics

Book edition 4th
Author(s) Randall D. Knight
Pages 1240 pages
ISBN 9780133942651

# The allowed energies of a simple atom are , , and 6.00 . An electron traveling with a speed of collides with the atom. Can the electron excite the atom to the stationary state? The stationary state? Explain.

The electron can excite the atom into the energy level but it cannot excite the atom into the energy level.

See the step by step solution

## Step:1 : Given information

The allowed energies of a simple atom are , , and .

An electron traveling with a speed of collides with the atom.

## Step 2: Calculation

We have a quantized system with three discrete energy levels and . An electron travelling with a speed equals to collides with that system. We want to know if the energy, for the electron, is sufficient to excite that system to and state. Our aim now is to find the total energy of the electron.

The electron's kinetic energy, travelling with, is

We will neglect the electrical potential interaction between that system, which is the atom, and the colliding electron, hence the total energy of the electron is

This excitation can occurs under the following condition:

Energy of The Electron

where is the energy difference between first and jth energy level in that system.

(satisfies the excitation condition) (doesn't satisfy the excitation condition )

As a result of the above analysis, the electron can excite the system from the first to the second energy level because it has an energy larger than the difference in energies between level 1 and 2, but it can't excite the system to third state.

Therefore:

The electron cannot excite the atom into energy level.