The energy of a photon can be related to its wavelength or frequency using the following equations:
Energy = Planck's constant (h) × frequency (ν) Energy = (Planck's constant × speed of light) / wavelength
To find the wavelength and frequency of a photon with an energy of 8.2 x 10^-19 J, we can rearrange the equations.
First, let's find the frequency (ν):
Energy = h × ν ν = Energy / h
Plugging in the given values:
ν = (8.2 x 10^-19 J) / (6.626 x 10^-34 J·s) ν ≈ 1.24 x 10^15 Hz
Now, let's find the wavelength (λ):
Energy = (h × c) / λ λ = (h × c) / Energy
Plugging in the known values:
λ = [(6.626 x 10^-34 J·s) × (2.998 x 10^8 m/s)] / (8.2 x 10^-19 J) λ ≈ 2.42 x 10^-7 meters λ ≈ 242 nm
Therefore, the wavelength of the photon is approximately 242 nm, and its frequency is approximately 1.24 x 10^15 Hz.