What is the wavelength of light that can cause a transition of an electron in the hydrogen atom from the orbit with
n = 6 to n = 8?(answer in µm)
To find the wavelength of light that can cause a transition from one orbit to another in the hydrogen atom, we can use the Rydberg formula. The formula is given as:
1/λ = R * (1/n1^2 - 1/n2^2)
where:
- λ is the wavelength of light
- R is the Rydberg constant (approximately 1.097 × 10^7 m^-1)
- n1 and n2 are the initial and final orbit numbers, respectively.
In this case, n1 = 6 and n2 = 8. We need to convert the wavelength to micrometers (µm), so we'll use the conversion factor that 1 µm = 10^-6 m.
Let's plug the values into the formula:
1/λ = (1.097 × 10^7 m^-1) * (1/6^2 - 1/8^2)
Simplifying further:
1/λ = (1.097 × 10^7 m^-1) * (1/36 - 1/64)
1/λ = (1.097 × 10^7 m^-1) * (16/576 - 9/576)
1/λ = (1.097 × 10^7 m^-1) * (7/576)
Solving for λ:
λ = 1 / [(1.097 × 10^7 m^-1) * (7/576)]
λ = 576 / [(1.097 × 10^7 m^-1) * 7]
λ ≈ 0.0825 µm
Therefore, the wavelength of light that can cause a transition of an electron in the hydrogen atom from the orbit with n = 6 to n = 8 is approximately 0.0825 µm.