To determine the wavelength associated with a photon of energy, you can use the equation:
E = hc/λ,
where E is the energy of the photon, h is the Planck constant (approximately 6.626 x 10^-34 J·s), c is the speed of light (approximately 299,792,458 m/s), and λ is the wavelength of the photon.
Rearranging the equation to solve for λ:
λ = hc/E.
Plugging in the values:
λ = (6.626 x 10^-34 J·s × 299,792,458 m/s) / (1E-17 J).
Note that the energy is given in joules, but we need to convert it to the same unit as Planck's constant (J·s).
λ ≈ (1.98 x 10^-8 J·m·s / 1E-17 J).
Simplifying the expression:
λ ≈ 1.98 x 10^-8 m = 19.8 nm.
Therefore, a photon with an energy of 1E-17 J is associated with a wavelength of approximately 19.8 nm.