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Q. 2

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 1174

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Short Answer

An electron in a rigid box absorbs light. The longest wavelength in the absorption spectrum is . How long is the box?

The longest wavelength in the absorption spectrum is so the box is .

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Step by Step Solution

Step 1: Given Information 

We have to given that the longest wavelength in the absorption spectrum is .

We need to find the length of the box.

Step 2: Simplify

Absorbing the photon with the longest wavelength will result in the transition of the electron from the ground state to the state, and that's because the photon with the longest wavelength is the one with the smallest energy, and the smallest energy difference between the two states happens between and states. The energy of levels of an electron in a rigid box is given by:

in order for the transition to take place, the incident photon must have an energy equal to the energy difference between and . Since,

the equation to isolate and substitute the numerical values of the different variables.

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