To calculate the wavelength of a photon given its energy, you can use the following equation:
E = h * c / λ
where: E is the energy of the photon, h is Planck's constant (approximately 4.136 x 10^-15 electron volt-seconds), c is the speed of light (approximately 2.998 x 10^8 meters per second), and λ is the wavelength of the photon.
In this case, the energy of the photon is given as 10,000 electron volts. We can convert electron volts to joules by multiplying by the conversion factor: 1 eV = 1.602 x 10^-19 J.
So, the energy (E) in joules becomes:
E = 10,000 eV * (1.602 x 10^-19 J/eV) = 1.602 x 10^-15 J
Substituting the values into the equation, we have:
1.602 x 10^-15 J = (4.136 x 10^-15 eV s) * (2.998 x 10^8 m/s) / λ
Rearranging the equation to solve for λ, we get:
λ = (4.136 x 10^-15 eV s) * (2.998 x 10^8 m/s) / (1.602 x 10^-15 J)
Evaluating the expression:
λ ≈ 2.426 x 10^-12 meters
Therefore, the wavelength of a photon with an energy of 10,000 electron volts is approximately 2.426 x 10^-12 meters (or 2.426 picometers).