Question

Suppose that at least 18.9 eV is needed to free an electron from a particular element, i.e., to ionize the atom. What is the lowest frequency photon which can accomplish this? And, what is the corresponding wavelength for that photon? Give frequency for answer 1 and wavelength for answer 2.

Answer 1

Calculate the wavelength of the photon needed to ionize the atom. The energy of a photon is given by:

E = 1243/λ

E = energy, λ = wavelength

Given values:

E = 18.9eV

Plug in and solve for λ:

18.9 = 1243/λ

λ = 65.8nm

Calculate the frequency of the photon associated with this wavelength. Apply this equation:

c = fλ

c = speed of light in a vacuum, f = frequency, λ = wavelength

Given values:

c = 3×10⁸m/s, λ = 65.8×10⁻⁹m

Plug in and solve for f:

3×10⁸ = f(65.8×10⁻⁹)

f = 4.56 petahertz