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Chapter 8: Problem 17

Calculate the wavelengths, in nanometers, of the first four lines of the Balmer series of the hydrogen spectrum, starting with the longest wavelength component.

Short Answer

Expert verified
The wavelengths in nanometers of the first four lines of the Balmer series, from longest to shortest wavelengths, are calculated by substituting each transition into the Rydberg formula.

Step by step solution

01

Identify Energy Levels

Identify the energy levels for each line in the Balmer series. Since the Balmer series corresponds to transitions to the n=2 level, the four lines represent transitions from levels n=3, n=4, n=5, and n=6 (since we start from the longest wavelength).
02

Calculate Wavelengths using the Rydberg Formula

Plug the energy levels into the Rydberg formula for each transition and calculate the resulting wavelength. Use R=1.097373 x 10⁷ m⁻¹ and Z=1. Convert the resulting wavelengths from meters to nanometers by multiplying by 1 x 10⁹.
03

Transition from n=3 to n=2

Calculate the wavelength for the transition from n=3 to n=2 by substituting into the Rydberg formula: 1/λ = R (1/2² - 1/3²). Solve for λ and convert the result to nanometers.
04

Transition from n=4 to n=2

Calculate the wavelength for the transition from n=4 to n=2: 1/λ = R (1/2² - 1/4²). Solve for λ and convert to nanometers.
05

Transition from n=5 to n=2

Calculate the wavelength for the transition from n=5 to n=2: 1/λ = R (1/2² - 1/5²). Solve for λ and convert to nanometers.
06

Transition from n=6 to n=2

Calculate the wavelength for the transition from n=6 to n=2: 1/λ = R (1/2² - 1/6²). Solve for λ and convert to nanometers.

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Most popular questions from this chapter

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Although Einstein made some early contributions to quantum theory, he was never able to accept the Heisenberg uncertainty principle. He stated, "God does not play dice with the Universe." What do you suppose Einstein meant by this remark? In reply to Einstein's remark, Niels Bohr is supposed to have said, "Albert, stop telling God what to do." What do you suppose Bohr meant by this remark?

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