Hydrogen atoms absorb energy so that the electrons are excited to n=4. Calculate the wavelength, in
nm, of the photon emitted when the electron relaxes to n=2.
487nm
O 456nm
4.56 x 10 nm
4.87 x 107nm

the wavelength, in nm, of the photon is 487.5 nm

Explanation:

Given:

n = 4 (excited)

n = 2 (relaxes)

Question: Calculate the wavelength, in nm, λ = ?

First, it is important to calculate the energy of the electron when it excited and then when it relaxes.

(excited)

(relaxes)

The change of energy

ΔE = E₁ - E₂=-0.85 - (-3.4) = 2.55 eV = 4.08x10⁻¹⁹J

For a photon, the wavelength emitted

Here

h = Planck's constant = 6.63x10⁻³⁴J s

c = speed of light = 3x10⁸m/s

Substituting values:

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