Question
It takes 463 kJ/mol to break an oxygen hydrogen single bond calculate the maximum wavelength of light which an oxygen hydrogen single bond could be broken by absorbing a single photon
Be sure your answer has correct number of significant digits in nm
Be sure your answer has correct number of significant digits in nm
Answers
GPT 3.5
To calculate the maximum wavelength of light needed to break an oxygen-hydrogen single bond, we can use the equation:
E = hc/λ
Where:
E = energy required to break the bond (in J)
h = Planck's constant = 6.62607015 × 10^-34 J·s
c = speed of light in vacuum = 2.998 × 10^8 m/s
λ = wavelength of light (in meters)
First, let's convert the energy required from kJ/mol to J/molecule:
1 kJ/mol = 1 kJ/ (6.022 × 10^23 molecules)
463 kJ/mol = (463 × 10^3 J) / (6.022 × 10^23 molecules)
463 kJ/mol = 7.686 × 10^-19 J/molecule
Now we can calculate the maximum wavelength:
E = hc/λ
7.686 × 10^-19 J/molecule = (6.62607015 × 10^-34 J·s)(2.998 × 10^8 m/s) / λ
Rearranging the equation to solve for λ:
λ = (6.62607015 × 10^-34 J·s)(2.998 × 10^8 m/s) / (7.686 × 10^-19 J/molecule)
Calculating the maximum wavelength:
λ ≈ 2.5885852 × 10^-7 meters
Converting meters to nanometers:
λ ≈ 2.5885852 × 10^-7 meters * (10^9 nm/1 meter)
λ ≈ 258.85852 nm
Therefore, the maximum wavelength of light required to break an oxygen-hydrogen single bond is approximately 258.9 nm (rounded to the correct number of significant digits).
E = hc/λ
Where:
E = energy required to break the bond (in J)
h = Planck's constant = 6.62607015 × 10^-34 J·s
c = speed of light in vacuum = 2.998 × 10^8 m/s
λ = wavelength of light (in meters)
First, let's convert the energy required from kJ/mol to J/molecule:
1 kJ/mol = 1 kJ/ (6.022 × 10^23 molecules)
463 kJ/mol = (463 × 10^3 J) / (6.022 × 10^23 molecules)
463 kJ/mol = 7.686 × 10^-19 J/molecule
Now we can calculate the maximum wavelength:
E = hc/λ
7.686 × 10^-19 J/molecule = (6.62607015 × 10^-34 J·s)(2.998 × 10^8 m/s) / λ
Rearranging the equation to solve for λ:
λ = (6.62607015 × 10^-34 J·s)(2.998 × 10^8 m/s) / (7.686 × 10^-19 J/molecule)
Calculating the maximum wavelength:
λ ≈ 2.5885852 × 10^-7 meters
Converting meters to nanometers:
λ ≈ 2.5885852 × 10^-7 meters * (10^9 nm/1 meter)
λ ≈ 258.85852 nm
Therefore, the maximum wavelength of light required to break an oxygen-hydrogen single bond is approximately 258.9 nm (rounded to the correct number of significant digits).