Question

The energy of the EM waves is of the order of $15\,keV$ . To which part of the spectrum does it belong?
A. $\gamma$ rays
B. $x$ rays
C. Infra-red rays
D. Ultraviolet rays

Answer 1

Here we have to use the relation between wavelength Planck’s constant and energy to find the spectrum.
Electromagnetic waves or EM waves are waves produced as a result of vibrations between an electrical field and a magnetic field.
In electromagnetic waves, the amplitude is the maximum field power of the electrical and magnetic fields. The wave energy is determined by the amplitude of the wave.

Complete step by step answer:
1. Gamma rays: Gamma or gamma radiation is a penetrating type of electromagnetic radiation originating from the radioactive decay of atomic nuclei. It consists of the shortest wavelength of electromagnetic waves, giving the maximum photon intensity. Its visible wavelength is in the range of $400\,nm$ to $700\,nm$ .
2. $x$ - rays: X-rays are a form of electromagnetic radiation, similar to visible light. Unlike light, however, x-rays have higher energy and can pass through most objects, including the body. Medical x-rays are used to generate images of tissues and structures inside the body.
The wavelength of $x -$ rays is in the range of $10\,nm$ to $0.001\,nm$ .
3. Infra-red rays: Infrared, also referred to as infrared light, is electromagnetic radiation of wavelengths greater than visible light. It is also usually opaque to the human eye, while IR at wavelengths of up to $1050$ nanometres from specially pulsed lasers can be seen by humans under some conditions.
4. Ultraviolet rays: Ultraviolet (UV) is a type of electromagnetic radiation with a wavelength from $10$ (with a corresponding frequency of about $30\,PHz$ ) to $400\,nm$ ( $750\,THz$ ), shorter than visible light, but longer than X-rays.

The energy for EM waves is given by:
$E = \dfrac{{hc}} {\lambda } \\\ = \dfrac{{1240\,eVnm}} {{15 \times {{10}^3}}} \\\ = 0.083\,nm \\\$
We know the visible range for $x -$ rays is between $10\,nm$ and $0.001\,nm$ , which belongs to the x-ray part of the spectrum.

So, the correct answer is “Option B”.

Note:
Here we have to multiply the Planck’s constant and speed of light to get the answer. Also we have to pay attention to the units otherwise we shall not get the desired answer. Not only can electromagnetic waves travel through air and solid objects, but through the vacuum of space as well. Also, electromagnetic waves do not lose energy while travelling.