Calculate the wavelength of light emitted when each of the following transitions occur in the hydrogen atom. What type of electromagnetic radiation is emitted in each transition? a. n = 4 → n = 3b. n = 5 → n = 4c. n = 5 → n = 3

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.