Answer:
It takes approximately
of energy to break one
single bond.
The maximum wavelength of a photon that can break one such bond is approximately
(in vacuum.) That's the same as
(rounded to three significant figures.)
Step-by-step explanation:
Energy per bond
The standard bond enthalpy of
single bonds is approximately
(note that the exact value can varies across sources.) In other words, it would take approximately
of energy to break one mole of these bonds.
The Avogadro Constant
gives the number of
bonds in one mole of these bonds. Based on these information, calculate the energy of one such bond:
.
Therefore, it would take approximately
of energy to break one
single bond.
Minimum frequency and maximum wavelength
The Einstein-Planck Relation relates the frequency
of a photon to its energy
:
.
The
here represents the Planck Constant:
.
A photon that can break one
single bond should have more than
of energy. Apply the Einstein-Planck Relation to find the frequency of a photon with exactly that much energy:
.
What would be the wavelength
of a photon with a frequency of approximately
? The exact answer to that depends on the medium that this photon is travelling through. To be precise, the exact answer depends on the speed of light in that medium:
.
In vacuum, the speed of light is
. Therefore, the wavelength of that
photon in vacuum would be:
.
(Side note: that wavelength corresponds to a photon in the ultraviolet region of the electromagnetic spectrum.)