Answer:
a. 1875 nm
b. 4051 nm
c. 1282 nm
These all are infrared electromagnetic radiation.
Explanation:
Our strategy here is to utilize the Rydberg equation for hydrogen atom electronic transition.
1/λ = Rh x (1/n₁² - 1/n₂²) where λ is the wavelength
Rh is Rydberg constant
n₁ and n ₂ are the energy levels ( n₁ < n₂ )
Now lets star the calculations.
a. n₁ = 3, n₂ = 4
1/λ = 1.097 x 10⁷ /m x (1/3² - 1/4²) = 5.333 x 10⁵/m
λ = 1/(5.333 x 10⁵ /m) = 1.875 x 10⁻⁶ m
Converting λ to nanometers:
1.875 x 10⁻⁶ m x (1 x10⁹ nm/m) = 1875 nm
b. n₁ = 4, n₂ = 5
1/λ = 1.097 x 10⁷ /m x (1/4² - 1/5²) = 2.468 x 10⁵/m
λ = 1/(2.468 x 10⁵/m) = 4.051 x 10⁻⁶ m
4.051 x 10⁻⁶ m x (1 x10⁹ nm/m) = 4051 nm
c. n₁ = 3, n₂ = 5
1/λ = 1.097 x 10⁷ /m x (1/3² - 1/5²) = 7801 x 10⁵/m
λ = 1/(7801 x 10⁵/m) = 1282 x 10⁻⁶ m
1282 x 10⁻⁶ m x (1 x10⁹ nm/m) = 1282 nm
All of these transitions fall in the infrared region of the spectrum.
