The free energy of a single electron falling through a potential difference of
one volt is 1 electronvolt (eV). Therefore, on a per electron basis, x volts → x eV.
Calculate the maximum wavelength of light (in nanometers) that provides enough
energy to an electron to participate in the water splitting reaction.
To calculate the maximum wavelength of light that provides enough energy for an electron to participate in the water splitting reaction, we need to use the relationship between energy and wavelength.
The energy of a photon is given by the equation:
E = hc/λ
Where E is the energy, h is Planck's constant (6.63 x 10^-34 J s), c is the speed of light (3 x 10^8 m/s), and λ is the wavelength.
We know that the energy required for an electron to participate in the water splitting reaction is 1 electronvolt (eV).
Now we can convert the energy from electronvolts to joules.
Since 1 eV is equal to 1.6 x 10^-19 J, the energy required for the reaction is:
E = 1.6 x 10^-19 J
Now we can rearrange the equation to solve for the wavelength (λ):
λ = hc/E
Plugging in the values:
λ = (6.63 x 10^-34 J s)(3 x 10^8 m/s) / (1.6 x 10^-19 J)
Simplifying the equation:
λ = 1.24375 x 10^-6 m
Lastly, we convert the wavelength to nanometers by multiplying by 10^9:
λ = 1.24375 x 10^-6 m x 10^9 nm/m
λ = 1.24375 x 10^3 nm
Therefore, the maximum wavelength of light that provides enough energy to an electron to participate in the water splitting reaction is approximately 1243.75 nm.