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Chapter 7: Problem 68

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
The electron in the hydrogen atom is initially excited to the \(n=5\) energy level and can transition to any of the lower energy levels (\(n=4, 3, 2, 1\)). There are 4 possible transitions (\(5 \rightarrow 4, 5 \rightarrow 3, 5 \rightarrow 2, 5 \rightarrow 1\)), so 4 different wavelengths of light can be emitted as the excited atom loses energy.

Step by step solution

01

Identify the possible transitions for the electron

The electron is initially in the n=5 energy level (also referred to as the 5th shell or principal quantum level). It can transition to any of the lower energy levels (n=4, 3, 2, or 1). Let's list the possible transitions: - 5 to 4 - 5 to 3 - 5 to 2 - 5 to 1
02

Count the number of transitions

Now that we have listed the possible transitions, let's count the number of different energy level transitions that can occur. We have: - One transition from 5 to 4 - One transition from 5 to 3 - One transition from 5 to 2 - One transition from 5 to 1 This gives us a total of 4 distinct energy level transitions.
03

Determine the number of wavelengths emitted as the atom loses energy

Since there are 4 distinct energy level transitions, the hydrogen atom can emit 4 different wavelengths of light as it loses energy. And remember, each of these transitions corresponds to a specific wavelength of light. So, the answer is 4 different wavelengths of light can be emitted as the excited hydrogen atom loses energy.

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