Question

What would be the maximum energy of an X-Ray if an electron is accelerated with a potential difference of 10kV. From this data find out the minimum wavelengths of the X-Ray. (Use hc = 1242 eV-nm)

• A. 100 keV and 100 nm
• B. 1000 keV and 1000 nm
• C. 10 keV and 0.1242 nm
• D. Can't be determined from the data given

Answer 1

The correct option is C

10 keV and 0.1242 nm

Accelerating potential is 100KV, hence the energy supplied to any electron is 100KeV. Now, when the electron loses this energy, the loss is shared by heat and X-Ray photon. If we think what maximum energy an X-Ray photon may have; it will be when all the share of loss goes in form of X-Ray.
i.e. all the energy of electron gets converted into an X-Ray photon.

Hence Maximum energy of X-Ray is 100KeV. Now, for X-Ray photons; $E=\frac{hc}{\lambda }$

Clearly, maximum energy means minimum wavelength. Hence ${\lambda }_{min}=\frac{hc}{E_{max}}=\frac{1242eV.nm}{10KeV}=\frac{1242eV.nm}{10000eV}=0.1242nm$