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.
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
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