It takes 412kJ/mol to break a carbon hydrogen single bond calculate the maximum wavelength of light for which a carbon hydrogen 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 required to break a carbon-hydrogen single bond, we need to use the equation:
E = hc/λ
where E is the energy of the photon, h is the 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 light.
First, let's convert the given energy of 412 kJ/mol to joules per molecule:
E = (412 kJ/mol) x (1000 J/1 kJ) / (6.022 x 10^23 mol^-1)
E = 6.834 x 10^-19 J
Now, we can rearrange the equation to solve for λ:
λ = hc/E
Substituting the values:
λ = (6.626 x 10^-34 J·s) * (2.998 x 10^8 m/s) / (6.834 x 10^-19 J)
λ = 2.911 x 10^-7 m
Since the question asks for the answer in nanometers (nm), let's convert the wavelength to nm:
λ = (2.911 x 10^-7 m) * (10^9 nm/1 m)
λ = 291.1 nm
Therefore, the maximum wavelength of light for which a carbon-hydrogen single bond could be broken by absorbing a single photon is 291.1 nm.
To calculate the maximum wavelength of light for which a carbon-hydrogen single bond could be broken by absorbing a single photon, we can use the equation:
E = hc/λ
Where:
E is the energy of the photon in joules,
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 light in meters.
First, we need to convert the energy required to break a carbon-hydrogen single bond from kJ/mol to joules. Since Avogadro's number is 6.022 x 10^23, we can calculate the energy per bond:
Energy per bond = (412 kJ/mol) / (6.022 x 10^23 bonds/mol)
≈ 6.839 x 10^-22 J
Now we can rearrange the equation to solve for the wavelength:
λ = hc / E
Substituting the known values:
λ = (6.626 x 10^-34 J·s) * (2.998 x 10^8 m/s) / (6.839 x 10^-22 J)
≈ 2.905 x 10^-6 m
Finally, we convert the wavelength from meters to nanometers by multiplying by 10^9:
λ (in nm) = (2.905 x 10^-6 m) * (10^9 nm/m)
≈ 2905 nm
Therefore, the maximum wavelength of light for which a carbon-hydrogen single bond could be broken by absorbing a single photon is approximately 2905 nm.
To calculate the maximum wavelength of light for which a carbon-hydrogen single bond could be broken by absorbing a single photon, we can use the relation E = hc/λ, where E is the energy of a single photon, h is Planck's constant (6.626 x 10^-34 J·s), c is the speed of light (3.00 x 10^8 m/s), and λ is the wavelength of light.
First, let's convert the energy given from kilojoules per mole (kJ/mol) to joules per molecule (J/mol). Since we only need the energy for a single photon, we divide by Avogadro's constant (6.022 x 10^23 molecules/mol) to get the energy per molecule:
Energy per molecule (J) = 412 kJ/mol / (6.022 x 10^23 molecules/mol)
Next, we convert the energy per molecule to energy per photon by dividing by the number of photons being absorbed, which is 1 in this case:
Energy per photon (J) = Energy per molecule (J) / 1
Now, we can rearrange the equation E = hc/λ to solve for the maximum wavelength (λ):
λ = hc/E
Substituting the values we have:
λ = (6.626 x 10^-34 J·s) * (3.00 x 10^8 m/s) / (Energy per photon in J)
Finally, we need to convert the wavelength from meters to nanometers by multiplying by 10^9:
Maximum wavelength (nm) = λ * 10^9
Now, let's plug in the values and calculate:
Maximum wavelength (nm) = [(6.626 x 10^-34 J·s) * (3.00 x 10^8 m/s)] / (Energy per photon in J) * 10^9
Make sure to substitute the value for "Energy per photon" accurately to get the correct result.