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Chapter 7: Problem 58

Assume that a hydrogen atom's electron has been excited to the \(n=5\) level. How many different wavelengths of light can be emitted as this excited atom loses energy?

Short Answer

Expert verified
A hydrogen atom's electron excited to the \(n=5\) level can lose energy by transitioning to lower energy levels (\(n=1\), \(n=2\), \(n=3\), and \(n=4\)). There are 4 possible transitions, and each will emit a photon with a different wavelength. Therefore, there are 4 different wavelengths of light that can be emitted as the atom loses energy.

Step by step solution

01

Identify the initial and final energy levels

Initially, the electron is in the n=5 energy level, and it can lose energy by transitioning to lower energy levels (n=1, n=2, n=3, and n=4).
02

Calculate the possible transitions

To find the total number of possible transitions, we can consider each lower energy level: 1. Transition from n=5 to n=4 2. Transition from n=5 to n=3 3. Transition from n=5 to n=2 4. Transition from n=5 to n=1 Each of these transitions will emit a photon with a different wavelength, so there are 4 different wavelengths possible.
03

Check for any additional transitions

It is essential to check if there are any other transitions involving intermediate energy levels. In this case, there are no additional transitions since all lower energy levels have been considered directly from n=5.
04

Answer the question

As calculated in Step 2, there are 4 different wavelengths of light that can be emitted when a hydrogen atom's electron transitions from the n=5 energy level to the lower energy levels (n=1, n=2, n=3, and n=4).

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