It takes 151 kJ/mol to break an iodine iodine single bond calculate the maximum wavelength of light for which an iodine iodine single bond could be broken by absorbing a single photon
Be sure your answer has correct number of significant digits
In nm
To calculate the maximum wavelength of light, we can use 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 light.
First, we need to convert the energy required to break the iodine-iodine single bond from kJ/mol to J/photon. There are Avogadro's number (6.022 x 10^23) of iodine-iodine single bonds in a mole:
Energy per photon = (151 kJ/mol) / (6.022 x 10^23) = 2.504 x 10^-22 J/photon
Now we can use the equation to solve for the maximum wavelength:
E = hc/λ
2.504 x 10^-22 J/photon = (6.626 x 10^-34 J*s)(2.998 x 10^8 m/s)/λ
Simplifying, we have:
2.504 x 10^-22 = 1.988 x 10^-25/λ
λ = 1.988 x 10^-25/2.504 x 10^-22
λ = 0.080 nm
Therefore, the maximum wavelength of light for which an iodine-iodine single bond could be broken by absorbing a single photon is approximately 0.080 nm.
To calculate the maximum wavelength of light required to break an iodine-iodine single bond, we can use the equation:
E = hc/λ
where:
E is the energy required to break the bond (in joules),
h is Planck's constant (6.62607015 x 10^-34 J·s),
c is the speed of light (299,792,458 m/s), and
λ is the wavelength of light (in meters).
First, let's convert the given energy from kJ/mol to J/mol:
151 kJ/mol x (1000 J/1 kJ) = 151000 J/mol
Next, we need to convert the energy per mole to energy per molecule, assuming we only need one photon to break the bond. Since Avogadro's number is 6.02214076 x 10^23 mol^-1, we divide the energy by Avogadro's number to get the energy per molecule:
151,000 J/mol ÷ (6.02214076 x 10^23 mol^-1) = 2.51 x 10^-19 J
Now we can rearrange the equation to solve for wavelength:
λ = hc/E
Plugging in the known values:
λ = (6.62607015 x 10^-34 J·s)(299,792,458 m/s) / (2.51 x 10^-19 J)
Calculating this expression, we find:
λ ≈ 7.88 x 10^-7 m
Finally, we convert the wavelength from meters to nanometers by multiplying by 10^9:
λ ≈ 7.88 x 10^-7 m x 10^9 nm/m = 788 nm
Therefore, the maximum wavelength of light for which an iodine-iodine single bond could be broken by absorbing a single photon is approximately 788 nm.