Considering the emission of the hydrogen atom,
a. what is the wavelength of the light emitted by the transition from n = 2 to n = 1.
b. In what region of the electromagnetic spectrum does this radiation belong?
Have a go and we will comment on the answer.
57
To determine the wavelength of light emitted during the transition of an electron in a hydrogen atom from one energy level to another, you can use the Rydberg formula. The Rydberg formula is given as:
1/λ = R * (1/n1^2 - 1/n2^2)
Where:
λ is the wavelength of light emitted,
R is the Rydberg constant (approximately 1.097 x 10^7 m^-1),
n1 is the initial energy level, and
n2 is the final energy level.
a. To find the wavelength of the light emitted by the transition from n = 2 to n = 1, we can substitute the values into the Rydberg formula:
1/λ = R * (1/1^2 - 1/2^2)
Simplifying further:
1/λ = R * (1 - 1/4)
1/λ = R * (3/4)
Now, rearrange the formula to solve for λ:
λ = 4R/3
Substituting the value of R:
λ = (4 * 1.097 x 10^7 m^-1) / 3
Calculating this expression, we find:
λ ≈ 3.65 x 10^-7 m
So, the wavelength of the light emitted during the transition from n = 2 to n = 1 is approximately 3.65 x 10^-7 meters.
b. To determine the region of the electromagnetic spectrum this radiation belongs to, we can analyze the wavelength range associated with different regions:
- Gamma rays: λ < 10^-11 m
- X-rays: 10^-11 m < λ < 10^-8 m
- Ultraviolet: 10^-8 m < λ < 4 x 10^-7 m
- Visible light: 4 x 10^-7 m < λ < 7 x 10^-7 m
- Infrared: 7 x 10^-7 m < λ < 10^-3 m
- Microwave: 10^-3 m < λ < 10^-1 m
- Radio waves: λ > 10^-1 m
Based on the calculated wavelength of approximately 3.65 x 10^-7 meters, the radiation belongs to the visible light region of the electromagnetic spectrum.