What potential difference must be applied across an X-ray tube to generate X-rays with a wavelength of no less than 0.10 nm ? Additionally, what is the maximum energy of a photon of this X-ray in joules?

Step-by-step solution

The minimum wavelength of X-rays produced in an X-ray tube is given by _ min = hc eV . Rearranging for the potential difference V : V = hc e _ min Using the value of hc 1240 eV nm : V = 1240 eV nm e 0.10 nm = 12400 V = 12.4 kV The maximum energy of an X-ray photon corresponds to the minimum wavelength: E_ max = hc _ min Substituting the standard values in SI units: E_ max = 6.63 10⁻³⁴ 3 10^8 0.10 10⁻⁹ E_ max = 19.89 10⁻¹⁶ J 2.0 10⁻¹⁵ J