Question

X-rays are produced in an X-ray tube operating at a given accelerating voltage.The wavelength of continuous X-ray has values from

• A. $0$ to $\infty$
• B. $0$ to ${\lambda }_{min}$ where ${\lambda }_{min}>0$
• C. $0$ to ${\lambda }_{max}$ where ${\lambda }_{max}<\infty$
• D. ${\lambda }_{min}$ to ${\lambda }_{max}$ , where ${\lambda }_{min}>0$ and ${\lambda }_{max}<\infty$

Answer 1

The correct option is D ${\lambda }_{min}$ to ${\lambda }_{max}$ , where ${\lambda }_{min}>0$ and ${\lambda }_{max}<\infty$

In an x-ray tube, electrons are accelerated in a vacuum by an electric field and shot into a piece of metal called the "target". X-rays are emitted as the electrons slow down (decelerate) in the metal. The output spectrum consists of a continuous spectrum of X-rays, with additional sharp peaks at certain energies (see graph on right). The spectrum has a sharp cutoff at low wavelength (high frequency), which is due to the limited energy of the incoming electrons. For example, if each electron in the tube is accelerated through 60 kV, then it will acquire a kinetic energy of 60 keV, and when it strikes the target it can create X-ray photons with energy of at most 60 keV, by conservation of energy. (This upper limit corresponds to the electron coming to a stop by emitting just one X-ray photon.
Usually the electron emits many photons, and each has an energy less than 60 keV.) A photon with energy of 60 keV or less has a wavelength of 21pm or more, so the X-ray spectrum has exactly that cutoff. Hence, the wavelength of continuous X-ray has values from
${\lambda }_{min}$ to ${\lambda }_{max}$ where ${\lambda }_{min}>0$ and ${\lambda }_{max}<\infty$.