Final answer:
To find the energy of an X-ray photon with a wavelength of 0.135nm in electron volts, one must use the equation E = (hc) / λ, where E is energy, h is Planck's constant, c is the speed of light, and λ is wavelength. After calculation, the photon's energy is approximately 9.13 keV.
Step-by-step explanation:
Calculating Energy of X-ray Photons
To calculate the energy of an X-ray photon with a wavelength of 0.135nm in electron volts (eV), we use the formula E = (hc) / λ, where E is energy, h is Planck's constant (6.626 x 10-34 J·s), c is the speed of light (3 x 108 m/s), and λ is the wavelength in meters. First, we convert the wavelength from nanometers to meters by multiplying by 10-9. Then, we can substitute the values into the formula to calculate the energy in Joules. Finally, we convert Joules to electron volts using the conversion 1 eV = 1.602 x 10-19 J.
Following these steps for the given wavelength:
- Wavelength in meters: 0.135nm = 0.135 x 10-9 m.
- Energy in Joules: E = (6.626 x 10-34 J·s * 3 x 108 m/s) / 0.135 x 10-9 m.
- Energy in eV: E (in Joules) / 1.602 x 10-19 J/eV.
After calculations, we find that the energy of the X-ray photon is approximately 9.13 keV.