Calculate the wavelength, λ, in meters of a photon capable of exciting an electron in He+ from the ground state to n = 4.
To calculate the wavelength, λ, of a photon capable of exciting an electron in He+ from the ground state to n=4, we can use the Rydberg formula. The Rydberg formula relates the wavelength of light emitted or absorbed by an atom to the energy levels of the atom.
The formula is given as:
1/λ = R * (1/n1^2 - 1/n2^2)
Where λ is the wavelength of the photon, R is the Rydberg constant, and n1 and n2 are the initial and final energy levels of the electron, respectively.
In this case, the initial energy level is the ground state (n1 = 1), and the final energy level is n=4 (n2 = 4). The Rydberg constant (R) is a known value:
R = 1.097373 x 10^7 m^-1
Substituting these values into the formula, we get:
1/λ = (1.097373 x 10^7 m^-1) * (1/1^2 - 1/4^2)
Simplifying the expression within the parentheses:
1/λ = (1.097373 x 10^7 m^-1) * (1 - 1/16)
1/λ = (1.097373 x 10^7 m^-1) * (15/16)
1/λ = 1.032857 x 10^7 m^-1
Now, we need to find the reciprocal of both sides of the equation:
λ = 1 / (1.032857 x 10^7 m^-1)
Calculating this, we find:
λ ≈ 9.6934 x 10^-8 meters
Therefore, the wavelength (λ) of the photon capable of exciting an electron in He+ from the ground state to n=4 is approximately 9.6934 x 10^-8 meters.