The Wavelength of Radiation Emitted in the Transition from the Third Excited State to Ground State in Hydrogen Atom

The wavelength of radiation emitted in the transition from the third excited state to the ground state in a hydrogen atom can be determined using the Rydberg formula:

Rydberg formula:
The Rydberg formula calculates the wavelength (λ) of the radiation emitted when an electron in a hydrogen atom transitions between two energy levels. It is given by the equation:

1/λ = R * (1/n₁² - 1/n₂²),

where λ is the wavelength of the emitted radiation, R is the Rydberg constant (approximately 1.097 × 10^7 m⁻¹), n₁ is the initial energy level, and n₂ is the final energy level.

Transition from the Third Excited State to Ground State:
In this case, the initial energy level (n₁) is the third excited state (n₁ = 3) and the final energy level (n₂) is the ground state (n₂ = 1).

Calculating the Wavelength:
Substituting the values into the Rydberg formula, we have:

1/λ = R * (1/3² - 1/1²)
= R * (1/9 - 1/1)
= R * (1/9 - 9/9)
= R * (-8/9)

To determine the wavelength (λ), we take the reciprocal of both sides of the equation:

λ = 9/(-8) * 1/R
≈ -9/8 * 1/(1.097 × 10^7 m⁻¹)
≈ -9/(8 * 1.097 × 10^7) m

The negative sign indicates that the radiation emitted is in the form of an electromagnetic wave.

Final Result:
The approximate wavelength of the radiation emitted when an electron in a hydrogen atom transitions from the third excited state to the ground state is approximately 9/(8 * 1.097 × 10^7) meters, with a negative sign indicating an electromagnetic wave.

Electron transmission method