It takes 348kJ/mol to break a carbon carbon single bond calculate the maximum wavelength of light for which a carbon carbon 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 that can break a carbon-carbon single bond, we will use the equation:
E = hc/λ
where:
E is the energy required to break the bond (348 kJ/mol),
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 we are trying to calculate.
First, let's convert the energy required to break the bond from kilojoules to joules:
E = 348 kJ/mol × (1000 J/1 kJ) = 348,000 J/mol
Now, we need to convert the energy per mole into energy per photon:
Avogadro's number (N_A) = 6.022 x 10^23 mol^-1
Energy per photon (E_photon) = E / N_A
E_photon = (348,000 J/mol) / (6.022 x 10^23 mol^-1) = 5.778 x 10^-19 J/photon
Now, we can rearrange the equation to solve for the wavelength:
λ = hc/E_photon
λ = (6.626 x 10^-34 J·s) × (2.998 x 10^8 m/s) / (5.778 x 10^-19 J/photon)
λ ≈ 3.84 x 10^-7 m or 384 nm
Therefore, the maximum wavelength of light for which a carbon-carbon single bond could be broken by absorbing a single photon is approximately 384 nm.
To calculate the maximum wavelength of light for which a carbon-carbon single bond could be broken by absorbing a single photon, we need to use the energy-wavelength relationship:
E = hc/λ
where:
E = energy of photon
h = Planck's constant (6.63 x 10^-34 J·s)
c = speed of light in a vacuum (3.00 x 10^8 m/s)
λ = wavelength of light
First, we need to convert the given energy of 348 kJ/mol to joules:
348 kJ/mol = 348 × 10^3 J/mol
Next, we convert the energy per molecule to energy per photon. Since 1 mole contains Avogadro's number of molecules (6.022 x 10^23), we divide the energy by Avogadro's number to get the energy per photon:
Energy per photon = 348 × 10^3 J/mol / (6.022 x 10^23)
Now we can plug the values into the equation to solve for the wavelength:
Energy per photon = hc/λ
λ = hc / Energy per photon
λ = (6.63 x 10^-34 J·s) × (3.00 x 10^8 m/s) / Energy per photon
Calculating the value of λ will give us the maximum wavelength in meters. To convert it to nanometers, we need to multiply by 10^9:
λ = [(6.63 x 10^-34 J·s) × (3.00 x 10^8 m/s) / Energy per photon] × 10^9
Now let's perform the calculation:
λ = [(6.63 x 10^-34 J·s) × (3.00 x 10^8 m/s) / (348 × 10^3 J/mol / (6.022 x 10^23)) ] × 10^9
Simplifying the expression:
λ = [(6.63 x 3.00 x 6.022) / (348 × 10^3) ] × 10^9
λ ≈ 114 nm
Therefore, the maximum wavelength of light for which a carbon-carbon single bond could be broken by absorbing a single photon is approximately 114 nm.
To calculate the maximum wavelength of light for which a carbon-carbon single bond could be broken by absorbing a single photon, we need to apply the concept of energy conversion.
The energy of a photon can be determined using the equation: E = hc/λ, where E is the energy of the photon, h is Planck's constant (6.62607015 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.
Now, we can convert the energy required to break the bond (348 kJ/mol) into Joules per photon:
1 kJ = 1000 J
1 mol = 6.02214076 x 10^23 particles
So, the energy per photon can be calculated as follows:
Energy per photon = (348 kJ/mol) / (6.02214076 x 10^23 particles/mol) * (1000 J/1 kJ) * (1 mol/1 photon)
Next, we can substitute this value into the energy equation mentioned earlier:
E = hc/λ
Rearranging the equation to solve for wavelength (λ):
λ = hc/E
Now we can calculate the maximum wavelength (λ) by substituting the values into the equation:
λ = (6.62607015 x 10^-34 J·s) * (2.998 x 10^8 m/s) / (Energy per photon)
Since we're looking for the answer in nanometers (nm), we need to convert the result to the appropriate unit:
1 m = 10^9 nm
Finally, convert the result from meters to nanometers:
Maximum wavelength = λ * (10^9 nm/1 m)
By following these calculations, you will obtain the maximum wavelength of light for which a carbon-carbon single bond could be broken by absorbing a single photon with the correct number of significant digits in nm.