Calculate the maximum wavelength of light capable of removing an electron for a hydrogen atom from the energy state characterized by the following
when n=4
=__________nm
So the two energy states are n=4 and n=inf
Use the Rydberg equation, right?
To calculate the maximum wavelength of light capable of removing an electron from a specific energy state in a hydrogen atom, we need to use the Rydberg formula. The Rydberg formula is given by:
1/λ = R * [(1/n_upper^2) - (1/n_lower^2)]
Where:
- λ is the wavelength of light (in meters)
- R is the Rydberg constant (approximately 1.097 × 10^7 m^-1)
- n_upper is the principal quantum number of the higher energy state
- n_lower is the principal quantum number of the lower energy state
In this case, we are given that n_upper = 4. Since we want to find the maximum wavelength, we consider the electron transition from n_lower to infinity. As n approaches infinity, 1/n_lower^2 becomes negligible, so we can approximate the equation as:
1/λ = R * (1/n_upper^2)
Now, substitute the given values:
1/λ = (1.097 × 10^7 m^-1) * (1/4^2)
Simplifying:
1/λ = (1.097 × 10^7 m^-1) * (1/16)
1/λ = 6.85625 × 10^5 m^-1
To find λ, take the reciprocal of both sides:
λ = 1 / (6.85625 × 10^5 m^-1)
Calculating:
λ ≈ 1.458 × 10^-6 meters (or 1.458 μm)
Therefore, the maximum wavelength of light capable of removing an electron from the n=4 energy state of a hydrogen atom is approximately 1.458 μm.