Enter the principal quantum number (n) into the calculator to determine the wavelength of light emitted by the electron transitioning to the second energy level in a hydrogen atom.

Balmer Rydberg Equation

The Balmer Rydberg equation is used to calculate the wavelength of light emitted during electron transitions in a hydrogen atom. The formula is given by:

λ = 1 / (R * (1 / 2² - 1 / n²))

Variables:

  • λ is the wavelength of light emitted (nm)
  • R is the Rydberg constant (1.0973731568508 x 10^7 m^-1)
  • n is the principal quantum number (n > 2)

To calculate the wavelength, input the principal quantum number (n) for the electron’s final energy level in the hydrogen atom. The initial energy level for the Balmer series is always 2.

What is the Balmer Rydberg Equation?

The Balmer Rydberg equation is a formula that predicts the wavelength of light resulting from an electron moving between energy levels in a hydrogen atom. Specifically, it applies to the Balmer series of the hydrogen spectrum, which involves transitions of an electron to the second energy level from higher levels (n > 2). The equation is a specific application of the more general Rydberg formula for the hydrogen spectral series.

How to Calculate Wavelength with the Balmer Rydberg Equation?

The following steps outline how to calculate the wavelength using the Balmer Rydberg equation.

  1. First, determine the principal quantum number (n) for the final energy level of the electron in the hydrogen atom.
  2. Ensure that the principal quantum number (n) is greater than 2, as the Balmer series involves transitions to the second energy level.
  3. Use the Balmer Rydberg equation: λ = 1 / (R * (1 / 2² – 1 / n²)).
  4. Calculate the wavelength (λ) in meters and then convert it to nanometers by multiplying by 1e9.
  5. After inserting the variable and calculating the result, check your answer with the calculator above.

Example Problem:

Use the following variable as an example problem to test your knowledge.

Principal quantum number (n) = 3

Using the Balmer Rydberg equation, calculate the wavelength of light emitted when an electron transitions from the third energy level to the second energy level in a hydrogen atom.