"The sun emits UV radiation that can have serious health consequences. In particular, so-called UVB radiation is mostly absorbed by the ozone layer in the upper atmosphere (altitudes of 10 - 50 km), but the part that reaches the earth can cause DNA mutations. The highest energy UVB photons have a wavelength of 320 nm. Calculate the energy of a single UVB photon (in Joules) and the energy of one mole of UVB photons (in kJ/mol)."
So, I'm pretty sure the first part of the question is unnecessary info. I think that I can calculate the energy in Joules by using E=hc/320nm. For that I'm getting 6.21 x 10^-19 J. I just need help finding the energy of one mole of UVB photons.
An explanation would be awesome, thanks in advance!
Your answer of 6.21E-19 J is correct. Obviously you used 320E-9 for the wavelength. For one mole just multiply that number by 6.02E23.
To calculate the energy of a single UVB photon in Joules, you can use the equation you mentioned: E = hc/λ, where E is the energy of the photon, h is Planck's constant (6.626 x 10^-34 J·s), c is the speed of light (3.00 x 10^8 m/s), and λ is the wavelength of the photon (320 nm or 3.20 x 10^-7 m).
Using these values, we can substitute them into the equation:
E = (6.626 x 10^-34 J·s) x (3.00 x 10^8 m/s) / (3.20 x 10^-7 m)
E = 1.96 x 10^-19 J
So, the energy of a single UVB photon is approximately 1.96 x 10^-19 Joules.
To find the energy of one mole of UVB photons, you need to multiply the energy of a single photon by Avogadro's number (6.022 x 10^23), which represents the number of particles in one mole of any substance.
Energy in 1 mole = (1.96 x 10^-19 J) x (6.022 x 10^23)
Energy in 1 mole = 1.18 x 10^5 J
However, it is common to express energies in kJ/mol, so we need to convert the energy to kJ by dividing by 1000:
Energy in 1 mole = 1.18 x 10^5 J / 1000
Energy in 1 mole = 118 kJ/mol
Therefore, the energy of one mole of UVB photons is approximately 118 kJ/mol.