What is the difference in energy for a photon of ultra-violet radiation, wavelength 319 nm and a photon of ultra-violet radiation, wavelength 238 nm.

To find the difference in energy between two photons of different wavelengths, you can use the equation:

E = hc/λ

where:
E is the energy of the photon,
h is the Planck's constant (approximately 6.626 × 10^-34 J·s),
c is the speed of light (approximately 3.00 × 10^8 m/s), and
λ is the wavelength of the photon.

Let's apply this equation to find the difference in energy between the two photons.

For the first photon with a wavelength of 319 nm (or 319 × 10^-9 m), we can calculate its energy as follows:

E1 = (6.626 × 10^-34 J·s * 3.00 × 10^8 m/s) / (319 × 10^-9 m)
E1 = 6.57 × 10^-19 J

Similarly, for the second photon with a wavelength of 238 nm (or 238 × 10^-9 m), we can calculate its energy:

E2 = (6.626 × 10^-34 J·s * 3.00 × 10^8 m/s) / (238 × 10^-9 m)
E2 = 8.32 × 10^-19 J

To find the difference in energy, subtract the energy of the first photon from the energy of the second photon:

ΔE = E2 - E1
ΔE = (8.32 × 10^-19 J) - (6.57 × 10^-19 J)
ΔE = 1.75 × 10^-19 J

Therefore, the difference in energy between a photon with a wavelength of 319 nm and a photon with a wavelength of 238 nm in the ultraviolet radiation is approximately 1.75 × 10^-19 J.