Calculate the wavelength of light emitted when each of the following transactions occur in the hydrogen atom.what type of electromagnetic radiation is emitted in each transion
Given information:
Atomic number, Z = 1 (Hydrogen atom)
(a) An electron moves from n = 5 to n = 3
Firstly, we can calculate the energy difference between the two energy levels using the Rydberg formula:
1/λ = RZ^2(1/nf^2 - 1/ni^2)
where λ is the wavelength of the emitted light, R is the Rydberg constant (1.097 x 10^7 m^-1), Z is the atomic number, nf is the final energy level (n = 3), and ni is the initial energy level (n = 5).
Plugging in the values:
1/λ = (1.097 x 10^7 m^-1) x 1^2 [(1/3^2) - (1/5^2)]
1/λ = 1.096 x 10^7 m^-1 x (0.1111 - 0.04)
1/λ = 1.096 x 10^7 m^-1 x 0.0711
1/λ = 778.72 x 10^2 m^-1
λ = 1.282 x 10^-6 m (or 1.282 micrometers)
The type of electromagnetic radiation emitted in this transition is infrared.
(b) An electron moves from n = 4 to n = 1
Using the same formula as above:
1/λ = RZ^2(1/nf^2 - 1/ni^2)
where λ is the wavelength of the emitted light, R is the Rydberg constant (1.097 x 10^7 m^-1), Z is the atomic number, nf is the final energy level (n = 1), and ni is the initial energy level (n = 4).
Plugging in the values:
1/λ = (1.097 x 10^7 m^-1) x 1^2 [(1/1^2) - (1/4^2)]
1/λ = 1.096 x 10^7 m^-1 x (0.25 - 0.0625)
1/λ = 1.096 x 10^7 m^-1 x 0.1875
1/λ = 2058.75 x 10^2 m^-1
λ = 4.857 x 10^-7 m (or 485.7 nanometers)
The type of electromagnetic radiation emitted in this transition is visible light (specifically, a shade of violet).
Note: The calculations are based on the assumption that the hydrogen atom is in its ground state.