Distinguish between soft X-rays and hard X-rays.

Hint: An X-ray, also known as X-radiation, is a form of high-energy electromagnetic radiation which is penetrating in nature. Most radiations are distinguished by their corresponding frequencies and wavelength. Thus the difference between hard and soft X-ray must be based on similar physical quantities.

Complete step by step answer:
When highly energetic electrons are made to strike a metal target, electromagnetic radiations are emitted from the target. A large part of this radiation has a wavelength of the order 0.1nm and these radiations are known as X-rays.
X-rays were discovered by a German physicist W C Roentgen in 1895.
A device used to produce X-rays is generally called an X-rays tube. In the process of X-ray generation a fraction of kinetic energy appears as the energy of photons varies from collision to collision. In a certain collision, the electron may lose its entire kinetic energy to bring out a photon or it may not create a photon at all. So the energy of the generated photon can lie anywhere between 0 to eV.
The maximum energy of a photon can be$E = eV$.
The wavelength of X-ray and the energy of the corresponding photon are related through the equation:
$\lambda = \dfrac{{hc}}{E}$
As E can take any value between 0 to eV, the wavelength, $\lambda $can take any value between infinity and $\dfrac{{hc}}{{eV}}$. This explains the origin of continuous X-rays and the cut-off wavelength, i.e.
${\lambda _{\min }} = \,\dfrac{{hc}}{{eV}}$
The X-rays of low wavelengths are called hard X-rays and those of larger wavelengths are called soft X-rays.
Soft X-rays are produced at comparatively lower potential difference than hard X-rays. They have a wavelength of $4\mathop A\limits^ \circ $ or above. They also have lower frequencies and hence lesser energy. Soft X-rays are also categorized with low penetrating power.
On the other hand hard X-rays have wavelengths of the order of $1\mathop A\limits^ \circ $. Also are associated with higher frequency and hence higher energy. As a consequence to all these characteristics they have high penetrating power.

Note: An easier way for students to memorize the difference between hard and soft X-rays is to associate the term “hard” with “more”. So hard X-rays are the ones with more energy. And by establishing that they have more energy, by the equation giving relation between wavelength and energy its will be clear that these quantities are inversely proportional. So higher the energy lower will be the wavelength.