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Chapter 4: Problem 12

Calculate the wavelengths of the first three lines in the Lyman series for hydrogen.

Short Answer

Expert verified
The wavelengths of the first three lines in the Lyman series for hydrogen are obtained using the formula for each with the respective values of n2. They are given by: 位1: 1 / (R * (1 - 1/4)), 位2: 1 / (R * (1 - 1/9)), 位3: 1 / (R * (1 - 1/16))

Step by step solution

01

Identify n1 and n2

For the Lyman series, n1 is always 1 because the transitions happen from higher energy levels down to the ground state. For the first three lines of the series, n2 will be 2, 3, and 4 respectively.
02

Use the Rydberg formula for the first line

Substitute n1=1 and n2=2 into the formula 1/位 = R * (1/n1虏 - 1/n2虏) to find the wavelength of the first line in the Lyman series. After substitution, it becomes 1/位 = R * (1 - 1/4).
03

Solve for the wavelength of the first line

After the calculation in Step 2, it's necessary to solve the formula for 位 to get the wavelength of the first line. 位 = 1 / (R * (1 - 1/4))
04

Repeat steps 2 and 3 for the second and third lines

Repeat Steps 2 and 3 but replace n2 with 3 for the second line and 4 for the third line. Calculate separately for each line's wavelength.

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