Question

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

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

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

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.

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.