Hydrogen atoms are excited by a laser to the n = 4 state and then allowed to emit. What is the maximum number of distinct emission spectral lines (lines of different wavelengths) that can be observed from this system? Calculate the wavelength of the 4 to 2 transition.

Question

Alonso Rojas

Chemistry

23 November, 20:40

Hydrogen atoms are excited by a laser to the n = 4 state and then allowed to emit. What is the maximum number of distinct emission spectral lines (lines of different wavelengths) that can be observed from this system? Calculate the wavelength of the 4 to 2 transition.

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Answers (1)

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Laila Blankenship · Answer 1

Solution for the problem:

The number of lines N = n (n-1) / 2 = 4*3/2 = 6

Using Rydberg formula for hydrogen: 1/λ = R (1/n₁² - 1/n₂²)

for R ≈ 1.097e7 / m

So plugging the given in the Rydberg formula:

1/λ = 1.097e7/m * (1/1² - 1/3²) = 9.751e6 / m

λ = 1.026e-7 m = 102.6 nm