These UV photons can break chemical bonds in your skin to cause sunburn—a form of radiation damage. If the 310 nm radiation provides exactly the energy to break an average chemical bond in the skin, estimate the average energy of these bonds in \rm kJ/mol.
What is \rm? This same notation shows up almost every day and most of us don't have a clue as to its meaning.
From what I can tell, \rm shows up when a question is cut and pasted from Mastering Chemistry, the online homework program. It must have to do with programming language because it doesn't show up in the original problem. It can be ignored for the sake of solving it.
blabity
To estimate the average energy of the chemical bonds in the skin, we need to make use of the energy provided by the 310 nm radiation.
The energy of a photon can be calculated using the equation:
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 (2.998 x 10^8 m/s) and λ is the wavelength of the radiation.
First, let's convert the wavelength from nm to meters:
λ = 310 nm × (1 m/1 x 10^9 nm) = 310 x 10^-9 m
Now, we can substitute the values into the equation to calculate the energy of the photon:
E = (6.626 x 10^-34 J·s)(2.998 x 10^8 m/s) / (310 x 10^-9 m)
E ≈ 6.414 x 10^-19 J
Next, we can convert the energy from joules to kilojoules (kJ):
1 J = 1 x 10^-3 kJ
E = 6.414 x 10^-19 J × (1 kJ/1 x 10^3 J)
E ≈ 6.414 x 10^-22 kJ
So, the energy of each photon with a wavelength of 310 nm is approximately 6.414 x 10^-22 kJ.
To estimate the average energy of the chemical bonds in the skin, we can look at the energy required to break an average chemical bond. This energy is typically on the order of tens to hundreds of kilojoules per mole (kJ/mol). Therefore, the estimated average energy of the chemical bonds in the skin is likely on the order of tens to hundreds of kilojoules per mole (kJ/mol).