What is the energy (in eV ) of a photon of visible light that has a wavelength of 500 nm ?
To calculate the energy of a photon, you can use the equation:
E = (hc) / λ
where E is the energy of the photon, h is the Planck constant (approximately 6.626 x 10^-34 J*s), c is the speed of light (approximately 3 x 10^8 m/s), and λ is the wavelength of the light.
First, convert the given wavelength from nanometers (nm) to meters (m):
500 nm = 500 x 10^-9 m
Now, substitute the values into the equation:
E = (6.626 x 10^-34 J*s * 3 x 10^8 m/s) / (500 x 10^-9 m)
Simplifying:
E = (6.626 x 3) / (500 x 10^-9) * 10^-34 x 10^8
E = 19.878 x 10^-26 / 5 x 10^-1
E = 3.976 x 10^-25 J
To convert the energy from joules to electron volts (eV), you can use the conversion factor:
1 eV = 1.6 x 10^-19 J
Now, calculate the energy in eV:
E = (3.976 x 10^-25 J) / (1.6 x 10^-19 J/eV)
Simplifying:
E ≈ 24.85 eV
Therefore, the energy of a photon of visible light with a wavelength of 500 nm is approximately 24.85 electron volts (eV).