Question

The energy E of the electron in a hydrogen atom can be calculated from the Bohr formula: R₂ 2 E=-- 71 In this equation R, stands for the Rydberg energy, and stands for the principal quantum number of the orbital that holds the electron. (You can find the value of the Rydberg energy using the Data button on the ALEKS toolbar.) Calculate the wavelength of the line in the emission line spectrum of hydrogen caused by the transition of the electron from an orbital with n = 11 to an orbital with n=7. Round your answer to 3 significant digits.​

Answer 1

The wavelength of a line in the emission line spectrum of hydrogen caused by the transition of an electron from an orbital with n = 11 to an orbital with n = 7 can be calculated using the Rydberg formula.

The Rydberg formula for the wavelength of the spectral line is:

1/λ = R(1/n₁² - 1/n₂²)

Where λ is the wavelength, R is the Rydberg constant, and n₁ and n₂ are the initial and final quantum numbers of the electron's orbit, respectively.

Substituting the given values of n₁ and n₂ into the equation and solving for λ:

1/λ = R(1/11² - 1/7²)
1/λ = R(0.0081 - 0.0370)
λ = 1/(R(0.0370 - 0.0081))

Since we don't know the value of R, we don't have enough information to calculate the wavelength of the line.