Question

Hydrogen atoms absorb energy so that the electrons are excited to n=4. Calculate the wavelength, in

Answer 1

Answer:

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.

$E_{1} =\frac{-13.6}{n^{2} } =\frac{-13.6}{4^{2} } =-0.85eV$ (excited)

$E_{2} =\frac{-13.6}{2^{2} } =-3.4eV$ (relaxes)

The change of energy

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

For a photon, the wavelength emitted

$\lambda =\frac{hc}{delta(E)}$

Here

h = Planck's constant = 6.63x10⁻³⁴J s

c = speed of light = 3x10⁸m/s

Substituting values:

$\lambda =\frac{6.63x10^{-34}*3x10^{8} }{4.08x10^{-19} } =4.875x10^{-7} m=487.5nm$