Answer:
λ = 233 nm
Step-by-step explanation:
Step 1: Data given
8.53 * 10^-19 J of energy needed to remove 1 electron
Step 2: Calculate the wavelength
The energy of a photon is proportional to its frequency.
Mathematically, the relationship between the energy of a photon and its frequency is described by the Planck - Einstein equation:
E = h*f
⇒ E = the energy of the photon
⇒ h = Planck's constant, equal to 6.626 * 10 ^-34 J*s
⇒ f = the frequency
Frequency and wavelength have an Inverse relationship and can be described by the equation:
f*λ = c
⇒ λ = the wavelength of the photon
⇒ c = the speed of light in a vacuum, usually given as 3 *10 ^8 m/s
ν *λ = c ⇒ ν = c /λ
E = h *c /λ
λ =( h ⋅*c )/E
λ = (6.626 * 10 ^-34 J*s * 3 *10 ^8 m/s) / 8.53 * 10^-19
λ = 2.33 *10^-7 m
λ = 233 nm
This wavelength places you in the ultraviolet - shortwave UV region of the EM spectrum.