Answers:
a) ![E_{Xrays}=1.19(10)^{6} kJ/mol](https://tex.z-dn.net/?f=E_%7BXrays%7D%3D1.19%2810%29%5E%7B6%7D%20kJ%2Fmol)
b)
c) X rays have the energy to disrupt organic compounds by breaking carbon–carbon single bonds, but AM radio waves not.
Explanation:
The energy of a photon in Joules is given by the following formula:
(1)
However, if we want to know this energy in units of
, we have to use the following formula:
(2)
<h2>
a) Now, in the case of X rays:</h2>
(3)
Where:
is the energy of X rays in Joules (
)
is the Planck constant
is the speed of light
is the wavelength of X rays
is the Avogadro's number
(4)
(5) This is the energy of X rays in units of kilojoules per mole
<h2>
b) For AM radio waves:</h2>
(6)
Where:
is the energy of AM radio waves in Joules (
)
is the wavelength of AM wavelength
(7)
(8) This is the energy of AM radio waves in units of kilojoules per mole
<h2>c) Which is able to disrupt
carbon–carbon single bonds?</h2>
If we compare the energy of both (X rays and AM radio waves) with the energy of a carbon–carbon single bond (
), we will have the following:
![1.19(10)^{6} kJ/mol > 1.19(10)^{-8} kJ/mol > 347 kJ/mol](https://tex.z-dn.net/?f=1.19%2810%29%5E%7B6%7D%20kJ%2Fmol%20%3E%201.19%2810%29%5E%7B-8%7D%20kJ%2Fmol%20%3E%20347%20kJ%2Fmol)
This means the energy of X rays is greater than the energy of AM radio waves and greater than the energy of carbon–carbon single bond as well:
![E_{Xrays} > E_{AM} > E_{carbon}](https://tex.z-dn.net/?f=E_%7BXrays%7D%20%3E%20E_%7BAM%7D%20%3E%20E_%7Bcarbon%7D)
In addition, this means X rays have the energy to disrupt organic compounds by breaking carbon–carbon single bonds, but AM radio waves not.