Radiation in the ultraviolet region of the electromagnetic spectrum is quite energetic. It is this radiation that causes dyes to fade and your skin to develop a sunburn. If you are bombarded with 1.00 mol of photons with a wavelength of 288 nm, what amount of energy, in kilojoules per mole of photons, are you being subjected to?
E = hc/wavelength.
Convert 288 nm to meters for wavelength.
The first equation is per photon; therefore, multiply the answer obtained by 6.022E23 for a mole, then change to kJ.
To determine the amount of energy (in kilojoules per mole of photons) you are being subjected to when bombarded with 1.00 mol of photons with a wavelength of 288 nm, we can use the energy equation relating wavelength and energy:
E = hc/λ
Where:
E is the energy of a single photon (in joules)
h is Planck's constant (6.63 × 10^-34 J·s)
c is the speed of light (3.00 × 10^8 m/s)
λ is the wavelength of the radiation (in meters)
1. First, we convert the given wavelength from nanometers (nm) to meters (m):
288 nm = 288 × 10^-9 m = 2.88 × 10^-7 m
2. Now, we can substitute the values into the energy equation:
E = (6.63 × 10^-34 J·s × 3.00 × 10^8 m/s) / (2.88 × 10^-7 m)
3. Calculate the energy of a single photon in joules:
E = 6.87 × 10^-19 J
4. To convert joules to kilojoules, divide by 1000:
E = 6.87 × 10^-19 J / 1000 = 6.87 × 10^-22 kJ
5. Finally, since you are bombarded with 1.00 mol of photons, multiply the energy per photon by Avogadro's number (6.022 × 10^23 mol^-1) to find the energy per mole of photons:
Energy per mole of photons = (6.87 × 10^-22 kJ) × (6.022 × 10^23 mol^-1)
6. Calculate the final answer:
Energy per mole of photons ≈ 4.14 kJ/mol
Therefore, you are being subjected to approximately 4.14 kilojoules per mole of photons when bombarded with 1.00 mol of photons with a wavelength of 288 nm.