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Q. 57

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 1116

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Short Answer

The first three energy levels of the fictitious element X were shown in FIGURE P38.56. An electron with a speed of 1.4 X 106 m/s collides with an atom of element X. Shortly afterward, the atom emits a photon with a wavelength of 1240 nm. What was the electron's speed after the collision? Assume that, because the atom is much more massive than the electron, the recoil of the atom is negligible. Hint: The energy of the photon is not the energy transferred to the atom in the collision.

The electron's speed after collision is

See the step by step solution

Step by Step Solution

Step 1: Given information

The first three energy levels of the fictitious element X were shown in FIGURE P38.56. An electron with a speed of 1.4 X 106 m/s collides with an atom of element X. Shortly afterward, the atom emits a photon with a wavelength of 1240 nm.

Step 2: Explanation

First we determine the energy of the photon:

Substitute the values:

This energy corresponds 32 transition, so after collision atom is in the n = 3 state. Before collision atom was in ground state (n = 1).|

Step 3: Calculations:

Energy which electron loses is:

Substitute the values:

The lost kinetic energy is given as:

Express in terms of Ekf

The expression for kinetic energy is:

Express in terms of vf:

Substitute the values:

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