Calculate the longest wavelength of the electromagnetic radiation emitted by the hydrogen atom in undergoing a transition from the n = 7 level.

#### Solution:

Show me the final answerâ†“

The electron will go from n = 7 to the n = 6 level. We will use the following equation to figure out the frequency.

(Where E is energy, h is Planck’s constant, and v is the frequency)

Since we know the electron undergoes a transition from n = 7 to n = 6, we can write the following:

(simplify by finding a common denominator)

\dfrac{-R_H}{49}\,-\,\dfrac{-R_H}{36}\,=\,\dfrac{13R_H}{1764}

We can now write the frequency emitted:

v\,=\,\dfrac{13R_H}{1764h}

v\,=\,\dfrac{13}{1764}\times \dfrac{2.179\times 10^{-18}\text{J}}{6.626\times 10^{-34}\text{J}\cdot \text{s}}

v\,=\,2.42\times 10^{13} /s

We can now figure out the wavelength by using the following equation:

(Where \lambda is the wavelength, c is the speed of light, v is the frequency)

\lambda\,=\,\dfrac{2.998\times 10^8\text{m/s}}{2.42\times 10^{13}/s}

\lambda\,=\,1.238\times 10^{-5} m

#### Final Answer:

why does the electron go from the 7th to the 6th? how do you get that information from the fact that it has the “longest wavelength”

This is actually in the book. The question also says it’s jumping a level from 7. Hope that helps ðŸ™‚