Exercise about determining energy of light that breaks bonds

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Discussion Overview

The discussion revolves around a homework exercise that involves calculating the energy of photons at different wavelengths to determine which types of light can break chemical bonds in biological molecules. The exercise specifically mentions infrared, visible, and ultraviolet light, and participants are engaged in clarifying the calculations required to relate photon energy to bond-breaking energy thresholds.

Discussion Character

  • Homework-related

Main Points Raised

  • One participant presents the exercise and attempts to calculate the energy of a photon at 150 nm, arriving at a value of 1.3252 * 10^(-17) J.
  • Another participant questions whether this value represents the energy of a single photon and suggests that it should be multiplied by Avogadro's number to find the energy in 1 mol of photons.
  • A subsequent reply confirms the need to multiply the energy of a single photon by Avogadro's number to obtain the total energy for 1 mol of photons.

Areas of Agreement / Disagreement

Participants appear to agree on the need to calculate the total energy for 1 mol of photons but have not yet reached a consensus on the specific calculations or the implications of the results.

Contextual Notes

The discussion does not clarify the assumptions regarding the conversion of energy units or the application of Avogadro's number in the calculations, which may affect the understanding of the results.

ducmod
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Homework Statement


Hello!
Here is the quote of the exercise:
Excessive exposure to sunlight increases the risk of
skin cancer because some of the photons have
enough energy to break chemical bonds in biological
molecules. These bonds require approximately
250–800 kJ / mol of energy to break. The energy of a
single photon is given by E = hc / lambda where E is the
energy of the photon in J, h is Planck’s constant 6.626 * 10^(-34) J s
and c is the speed of light 3 * 10^8 m/s
Determine which kinds of light
contain enough energy to break chemical bonds in
biological molecules by calculating the total energy
in 1 mol of photons for light of each wavelength.
(a) infrared light (1500 nm)
(b) visible light (500 nm)
(c) ultraviolet light (150 nm)

Of course, everyone knows that it's ultraviolet, but I can't come up with a correct math. Please, explain
my mistakes:
(6.626 * 10^(-34) J s * 3 * 10^8 m/s) / (150 * 10^(-9)) = 1.3252 * 10^(-17)
which I don't see how to fit in 250–800 kJ / mol of energy

Thank you!
 
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ducmod said:
in 1 mol of photons
 
Do you mean that 1.3252 * 10^(-17) is for one photon, and I have to multiply this number by avogadro number?
I didn't quite understand your remark.
 
ducmod said:
Do you mean that 1.3252 * 10^(-17) is for one photon, and I have to multiply this number by avogadro number?

That's exactly what you are asked to calculate, aren't you?
 

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