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
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).
To calculate the maximum wavelength (λ) of light required to break an oxygen-hydrogen single bond, we can use the equation:
energy (E) = Planck's constant (h) × speed of light (c) / wavelength (λ)
First, let's convert the given energy of 463 kJ/mol to joules per molecule:
1 kJ/mol = 1000 J/6.022 × 10²³ molecules
Energy (E) = 463 kJ/mol × (1000 J/6.022 × 10²³ molecules) = 7.679 × 10⁻²¹ J/molecule
Now, we can rearrange the equation to solve for wavelength (λ):
wavelength (λ) = Planck's constant (h) × speed of light (c) / energy (E)
Plugging in the known values:
λ = (6.626 × 10⁻³⁴ J·s) × (2.998 × 10⁸ m/s) / (7.679 × 10⁻²¹ J)
Calculating the result:
λ = 8.627 × 10⁴ m
Finally, let's convert the wavelength to nanometers:
1 m = 10⁹ nm
λ = 8.627 × 10⁴ m × (10⁹ nm / 1 m) = 8.627 × 10¹³ nm
Therefore, the maximum wavelength of light required to break an oxygen-hydrogen single bond by absorbing a single photon is approximately 8.63 × 10¹³ nm.
To calculate the maximum wavelength of light required to break an oxygen-hydrogen single bond, we need to use the equation:
E = hc/λ
Where:
E is the energy of a photon
h is Planck's constant (6.626 x 10^-34 J s)
c is the speed of light (3.0 x 10^8 m/s)
λ is the wavelength of light in meters
First, we need to convert the energy required to break the bond from kJ/mol to joules per molecule:
Energy per molecule = Energy per mole / Avogadro's number
Energy per molecule = 463 kJ/mol / (6.022 x 10^23 molecules/mol)
Next, we can calculate the energy of a single photon:
Energy per photon = Energy per molecule / number of molecules per photon
Energy per photon = Energy per molecule / 1
Now, we can rearrange the equation to solve for the wavelength:
λ = hc / E
Plugging in the values:
λ = (6.626 x 10^-34 J s * 3.0 x 10^8 m/s) / Energy per photon
Calculate the numerical value for Energy per photon:
Numerical value = Energy per photon * (6.022 x 10^23 molecules/mol)
Finally, convert the wavelength from meters to nanometers:
Wavelength (nm) = λ * 10^9
Follow these steps to perform the actual calculations and obtain the maximum wavelength in nanometers.