Answer
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Hint:When charged particles pass through any matter or vacuum, due to the changing electric and magnetic fields in the medium, there is a form of energy produced due to that disturbance. This disturbance or form of energy produced is known as electromagnetic radiation.
Formula used:
Expression of energy of an electromagnetic radiation,
\[E = h\nu \]……(i)
Where ‘h’ is Planck’s constant and \[\nu \] is the frequency of light.
Complete step by step solution:
Given that the electromagnetic radiation has an energy of 13.2 keV. In order to describe the behaviour of the charged particles in a medium or to find the energy, the formula for Planck’s constant will be used, according to which;
\[E = h\nu \]……(i)
The equation (i) can also be written as:
\[E = \dfrac{{hc}}{\lambda }\]
Now in order to find out the region in which the electromagnetic radiation belongs to, we need to calculate the wavelength. So, above definition can be written as,
\[\lambda = \dfrac{{hc}}{E}\]
Substituting the values and solving, we get
\[\lambda = \dfrac{{12400}}{{13.2 \times {{10}^3}}}\]
\[\Rightarrow \lambda = 0.939{A^ \circ }\]
\[\therefore \lambda \approx 1{A^ \circ }\]
Therefore, an electromagnetic radiation of energy 13.2 keV belongs to X-Ray region as the range of wavelength for X-Rays is \[{10^{ - 8}}m\,to\,{10^{ - 13}}m\].
Hence, option D is the correct answer.
Note: It is to be noted that in electromagnetic radiation, photons are released which carry energy. Photons are invisible particles and the energy released by the waves is in the form of small packets known as photons which can be calculated using Planck’s constant. It was proved by Maxwell, that the energy that is released is not continuous and the energy of each photon is directly proportional to the frequency of the waves.
Formula used:
Expression of energy of an electromagnetic radiation,
\[E = h\nu \]……(i)
Where ‘h’ is Planck’s constant and \[\nu \] is the frequency of light.
Complete step by step solution:
Given that the electromagnetic radiation has an energy of 13.2 keV. In order to describe the behaviour of the charged particles in a medium or to find the energy, the formula for Planck’s constant will be used, according to which;
\[E = h\nu \]……(i)
The equation (i) can also be written as:
\[E = \dfrac{{hc}}{\lambda }\]
Now in order to find out the region in which the electromagnetic radiation belongs to, we need to calculate the wavelength. So, above definition can be written as,
\[\lambda = \dfrac{{hc}}{E}\]
Substituting the values and solving, we get
\[\lambda = \dfrac{{12400}}{{13.2 \times {{10}^3}}}\]
\[\Rightarrow \lambda = 0.939{A^ \circ }\]
\[\therefore \lambda \approx 1{A^ \circ }\]
Therefore, an electromagnetic radiation of energy 13.2 keV belongs to X-Ray region as the range of wavelength for X-Rays is \[{10^{ - 8}}m\,to\,{10^{ - 13}}m\].
Hence, option D is the correct answer.
Note: It is to be noted that in electromagnetic radiation, photons are released which carry energy. Photons are invisible particles and the energy released by the waves is in the form of small packets known as photons which can be calculated using Planck’s constant. It was proved by Maxwell, that the energy that is released is not continuous and the energy of each photon is directly proportional to the frequency of the waves.
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