To determine the wavelength of a photon with a given energy, you can use the following equation:
λ = hc / E
where λ is the wavelength, h is Planck's constant (approximately 6.626 x 10^-34 J·s), c is the speed of light in a vacuum (approximately 2.998 x 10^8 m/s), and E is the energy of the photon.
First, let's convert the energy from electron volts (eV) to joules (J). Since 1 eV is equal to 1.602 x 10^-19 J, we can calculate:
E = 0.30 eV × (1.602 x 10^-19 J/eV) = 4.806 x 10^-20 J
Now, we can substitute the values into the equation to find the wavelength:
λ = (6.626 x 10^-34 J·s × 2.998 x 10^8 m/s) / (4.806 x 10^-20 J)
Simplifying the expression:
λ = 4.135 x 10^-7 m
To convert this to nanometers (nm), we multiply by 10^9:
λ = 4.135 x 10^-7 m × 10^9 nm/m = 413.5 nm
Therefore, the wavelength of a photon with an energy of 0.30 eV is approximately 413.5 nanometers (nm).