It takes 163kJ/mol to break an nitrogen-nitrogen single bond calculate the maximum wavelength of light for which nitrogen-nitrogen 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 nitrogen-nitrogen single bond, we will use the equation:
E = hc/λ
Where:
E = energy required to break the bond = 163 kJ/mol = 163 x 10^3 J/mol
h = Planck's constant = 6.626 x 10^-34 J·s
c = speed of light = 2.998 x 10^8 m/s
λ = wavelength of light required
Rearranging the equation, we get:
λ = hc/E
Substituting the given values:
λ = (6.626 x 10^-34 J·s * 2.998 x 10^8 m/s) / (163 x 10^3 J/mol)
λ = (1.983 x 10^-25 J·m) / (163 x 10^3 J/mol)
λ ≈ 1.22 x 10^-28 m
To express the answer in nm, we convert meters to nanometers by multiplying by 10^9.
λ ≈ 1.22 x 10^-19 nm
The maximum wavelength of light required to break a nitrogen-nitrogen single bond is approximately 1.22 x 10^-19 nm.
To calculate the maximum wavelength of light required to break a nitrogen-nitrogen single bond, we can use the equation:
E = hc/λ
Where:
E = energy required to break the bond (in Joules)
h = Planck's constant (6.62607015 × 10^-34 J*s)
c = speed of light (2.998 × 10^8 m/s)
λ = wavelength of light (in meters)
First, we need to convert the given energy of 163 kJ/mol to Joules per molecule.
1 mole of N2 molecules = 6.022 × 10^23 molecules
163 kJ/mol = 163 × 10^3 J/mol
So, the energy required to break a single nitrogen-nitrogen bond is:
163 × 10^3 J/mol ÷ 6.022 × 10^23 molecules = 2.71 × 10^-19 J
Now, we can rearrange the equation to solve for the wavelength:
λ = hc/E
Plugging in the values:
λ = (6.62607015 × 10^-34 J*s) × (2.998 × 10^8 m/s) / (2.71 × 10^-19 J)
λ ≈ 7.31 × 10^-7 m
Finally, we can convert the wavelength to nanometers:
λ ≈ 731 nm
Therefore, the maximum wavelength of light for which the nitrogen-nitrogen single bond could be broken by absorbing a single photon is approximately 731 nm.