What is the wavelength (in nm) for a photon of light with an energy of 3.20 x 10-19 J/photon?
To find the wavelength of a photon of light with a given energy, you can use the equation:
E = hc/λ
Where:
E is the energy of the photon (in joules)
h is Planck's constant (approximately 6.626 x 10^-34 J·s)
c is the speed of light in a vacuum (approximately 3.00 x 10^8 m/s)
λ is the wavelength of the photon (in meters)
First, let's convert the energy into joules:
3.20 x 10^-19 J/photon = 3.20 x 10^-19 J
Now, rearrange the equation to solve for λ:
λ = hc/E
Substitute the values:
λ = (6.626 x 10^-34 J·s * 3.00 x 10^8 m/s) / (3.20 x 10^-19 J)
Calculating this gives:
λ ≈ 6.20 x 10^-7 meters.
To convert meters to nanometers, multiply by 10^9:
λ ≈ 620 nm.
Therefore, the wavelength of a photon with an energy of 3.20 x 10^-19 J/photon is approximately 620 nm.
To find the wavelength of a photon of light, you can use the equation:
E = hc/λ
where E is the energy of the photon, h is Planck's constant (6.626 x 10^-34 J·s), c is the speed of light (3.00 x 10^8 m/s), and λ is the wavelength of the photon.
First, let's convert the energy from joules to electron volts (eV). 1 eV is equal to 1.602 x 10^-19 J.
E (eV) = (3.20 x 10^-19 J/photon) / (1.602 x 10^-19 J/eV) = 2
So, the energy of the photon is 2 eV.
Now, let's solve for λ:
λ = hc/E (eV)
Substituting the known values:
λ = (6.626 x 10^-34 J·s * 3.00 x 10^8 m/s) / (2 eV * 1.602 x 10^-19 J/eV)
Calculating:
λ ≈ 2.48 x 10^-7 m
To convert from meters to nanometers, multiply by 10^9:
λ ≈ 2.48 x 10^-7 m * 10^9 nm/m
λ ≈ 248 nm
Therefore, the wavelength of the photon is approximately 248 nm.