To find the wavelength (λ) and frequency (ν) of a photon with an energy of 8.2 x 10^-19 J, we can use the equation E = hc/λ, where E is the energy, h is Planck's constant, c is the speed of light, λ is the wavelength, and ν is the frequency.
Given: E = 8.2 x 10^-19 J h ≈ 6.626 x 10^-34 J·s (Planck's constant) c ≈ 3 x 10^8 m/s (speed of light)
First, rearrange the equation to solve for the wavelength:
E = hc/λ
λ = hc/E
Substitute the values:
λ = (6.626 x 10^-34 J·s * 3 x 10^8 m/s) / (8.2 x 10^-19 J)
λ = 2.419 x 10^-6 m
To convert the wavelength from meters to nanometers, multiply by 10^9:
λ = 2.419 x 10^-6 m * 10^9 nm/m
λ ≈ 2,419 nm
Therefore, the wavelength of the photon is approximately 2,419 nm.
To find the frequency, we can use the relationship between wavelength and frequency:
c = λν
Rearranging the equation to solve for frequency:
ν = c/λ
Substitute the values:
ν = (3 x 10^8 m/s) / (2.419 x 10^-6 m)
ν ≈ 1.24 x 10^14 Hz
Therefore, the frequency of the photon is approximately 1.24 x 10^14 Hz.