What is the wavelength of light that is emitted when an excited electron in the hydrogen atom falls from n = 5 to n = 1?

9.49 x 10⁻⁸ m

Explanation:

Data given:

excitation of electron = n-5 to n-1

wavelength of light = ?

Solution:

As the transition of electron take place from one level to other so the problem will be solved by using Rydberg's equation

Rydberg's equation

1/λ = R [1/n² (final) - 1/n² (initial) ]

where

R = Rydberg's constant = 1.0974 x 10⁷ m⁻¹

λ = wavelength

n (final) = the final energy level

n (initial) = the initial energy level

Now

Put the values in Rydberg's equation

1/λ = R [1/n² (final) - 1/n² (initial) ]

1/λ = 1.0974 x 10⁷ m⁻¹ (1/1² - 1/5²)

1/λ = 1.0974 x 10⁷ m⁻¹ (1/1 - 1/25)

1/λ = 1.0974 x 10⁷ m⁻¹ (1 - 0.04)

1/λ = 1.0974 x 10⁷ m⁻¹ (0.96)

1/λ = 1.0535 x 10⁷ m⁻¹

λ = 1 / 1.0535 x 10⁷ m⁻¹

λ = 9.49 x 10⁻⁸ m

the wavelength of light that is emitted = 9.49 x 10⁻⁸ m