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
Responses
Chemistry!! - bobpursley, Wednesday, October 22, 2008 at 4:05am
So the two energy states are n=4 and n=inf
Use the Rydberg equation, right?
yes this is the right equation- but idk why you use this and why u know from the problem to use 1/infinity...
If you REMOVE an electron from hydrogen, you move it to infinity (or at least so far away it may as well be at infinity). But putting infinity into the Rydberg equation gives you 1/infinity for that part of the equation and 1/infinity = 0.
To calculate the maximum wavelength of light capable of removing an electron for a hydrogen atom from the energy state characterized by n = 4, you need to use the Rydberg equation. The Rydberg equation is used to calculate the wavelengths of light emitted or absorbed by hydrogen atoms.
The Rydberg equation is given by:
1/λ = R(1/n1^2 - 1/n2^2)
where λ is the wavelength of light, R is the Rydberg constant, and n1 and n2 are the principal quantum numbers of the energy levels.
In this case, we are interested in finding the maximum wavelength of light, which corresponds to the minimum energy required to remove an electron from the atom. This occurs when the final energy state is at infinity, where n2 approaches infinity.
So, in the Rydberg equation, we replace n2 with infinity:
1/λ = R(1/4^2 - 1/infinity^2)
Since 1/infinity is approaching zero, we can ignore it in the equation, giving us:
1/λ = R(1/4^2)
Simplifying further:
1/λ = R/16
To find the maximum wavelength, we need to find the minimum value of the denominator, which occurs when R is the smallest possible value. The Rydberg constant, R, is approximately 1.097 x 10^7 m^-1.
So, substituting the values:
1/λ = (1.097 x 10^7 m^-1)/16
Solving for λ:
λ = 16/(1.097 x 10^7 m^-1)
λ ≈ 1.460 x 10^-7 m
To convert meters (m) to nanometers (nm), multiply the value by 10^9:
λ ≈ 1.460 x 10^-7 m x 10^9 nm/m
λ ≈ 1460 nm
Therefore, the maximum wavelength of light capable of removing an electron from the n = 4 energy state of a hydrogen atom is approximately 1460 nm.