Assertion: Soft and hard X− rays differ in frequency as well as velocity.
Reason: The penetrating power of hard X−rays is more than the penetrating power of soft X−rays.
A. If both assertion and reason are true and the reason is the correct explanation of the assertion.
B. If both assertion and reason are true but reason is not the correct explanation of the assertion.
C. If the assertion is true but the reason is false.
D. If the assertion and reason both are false
E. If assertion is false but the reason is true

Hint: Hard X-rays have higher energy than soft X-rays, which have lower energies. The energy has an inverse relationship with wavelength and is directly proportional to frequency. Therefore, the wavelength is shorter and the frequency is higher when the energy is larger.

Formula used:
The relationship between the matching photon's energy and X-ray wavelength is,
$E = \dfrac{{hc}}{\lambda }$
Here, $c$ is the speed of light, $\lambda$ is the wavelength of X-ray and $h$ is Planck's constant.

Complete step by step solution:
The high energy electromagnetic spectrum includes X-rays. X-rays have a shorter wavelength than visible rays because they are more energetic (since energy is inversely proportional to wavelength). Many objects, including the body, are transparent to them. As a result, they are employed to produce images of bones and tissues. The relationship between the matching photon's energy and X-ray wavelength is:
$E = \dfrac{{hc}}{\lambda }$

Larger wavelength X-rays are referred to as soft X-rays, while those with lower wavelengths are known as hard X-rays. Comparatively speaking, soft X-rays are generated at a lower potential difference than hard X-rays. They have a wavelength of $4\mathop A\limits^ \circ $ or above. Additionally, they have lower frequencies, which means less energy. Low penetrating power is another classification for soft X-rays.

On the other hand, hard X-rays have wavelengths in the order of $1\mathop A\limits^ \circ $ are additionally linked to higher frequency, and hence, higher energy. Because of all these qualities, they have a great penetrating power. The only difference between soft and hard X-rays is frequency. However, both kinds of X move at the speed of light.

Hence option E is correct.

Note: Making the word "hard" synonymous with the word "more" will help students remember the distinction between hard and soft X-rays. Therefore, hard X-rays have higher energy. And once it is shown that they have greater energy, it will be obvious that the relationship between these two variables—wavelength and energy—is inverse. Thus, the wavelength will be shorter the higher the energy.