It takes 945kJ/mol to break a nitrogen nitrogen triple bond calculate the maximum wavelength of light for which a nitrogen nitrogen triple 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 for breaking a nitrogen-nitrogen triple bond, we can use the equation:
E = hc/λ
where E is the energy in Joules, h is the Planck 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 in meters.
First, we need to convert the energy from kilojoules per mole (kJ/mol) to Joules per molecule (J). Since we are considering a single molecule, we divide 945 kJ/mol by Avogadro's number (6.022 x 10^23 molecules/mol) to get the energy per molecule:
E = (945 kJ/mol / 6.022 x 10^23 molecules/mol) = 1.571 x 10^-21 J
Next, we can solve the equation for λ:
λ = hc/E
λ = (6.626 x 10^-34 J*s * 2.998 x 10^8 m/s) / (1.571 x 10^-21 J)
λ = 1.261 x 10^-6 m
Finally, we convert the wavelength from meters to nanometers by multiplying by 10^9:
λ = 1.261 x 10^-6 m * 10^9 nm/1 m = 1.261 nm
Therefore, the maximum wavelength of light for which a nitrogen-nitrogen triple bond could be broken by absorbing a single photon is approximately 1.261 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 the Planck constant (6.62607015 × 10^-34 J⋅s), c is the speed of light (2.998 × 10^8 m/s), and λ is the wavelength of light.
First, we need to convert the given energy of 945 kJ/mol into joules. Since 1 kJ = 1000 J, we have:
Energy = 945 kJ/mol = 945 × 1000 J/mol
To convert from energy per mole to energy per photon, we need to use Avogadro's number (6.022 × 10^23 mol^-1). Therefore:
Energy per photon = (945 × 1000 J/mol) / (6.022 × 10^23 mol^-1) = 1.571 × 10^-20 J/photon
Now we can rearrange the equation to solve for the wavelength of light:
λ = hc/E
Plugging in the values, we have:
λ = (6.62607015 × 10^-34 J⋅s × 2.998 × 10^8 m/s) / (1.571 × 10^-20 J/photon)
Calculating this:
λ ≈ 3.985 × 10^-7 m
To convert this to nanometers (nm), we multiply by a conversion factor:
λ = (3.985 × 10^-7 m) × (10^9 nm/m)
Calculating this:
λ ≈ 398.5 nm
Therefore, the maximum wavelength of light for which a nitrogen-nitrogen triple bond could be broken by absorbing a single photon is approximately 398.5 nm (with the correct number of significant digits).
To calculate the maximum wavelength of light for which a nitrogen-nitrogen triple 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, 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 from kJ/mol to J/molecule. Since there is one mole in 6.022 x 10^23 molecules (Avogadro's number), we can divide the given energy by Avogadro's number to get the energy per molecule:
Energy per molecule = 945 kJ/mol / (6.022 x 10^23 molecules/mol)
Now, let's convert the energy per molecule to Joules:
Energy per molecule = 945 x 10^3 J/mol / (6.022 x 10^23 molecules/mol)
Next, we need to convert the energy per molecule to energy per photon. Since we are considering the absorption of a single photon, we divide the energy per molecule by Avogadro's number:
Energy per photon = (945 x 10^3 J/mol) / (6.022 x 10^23 molecules/mol x 6.022 x 10^23 photons/mol)
Now, we have the energy per photon in Joules. To find the maximum wavelength, we can substitute the values into the equation E = hc/λ and solve for λ:
λ = hc/E
Substituting the known values:
λ = (6.626 x 10^-34 J.s) x (3.00 x 10^8 m/s) / (Energy per photon)
Finally, we can calculate the maximum wavelength in meters and convert it to nanometers by multiplying by 10^9:
Maximum wavelength = λ x 10^9 nm
By following this process, you can calculate the maximum wavelength of light for which a nitrogen-nitrogen triple bond could be broken by absorbing a single photon.