Question

In the coolidge tube the potential difference between the cathode and anticathode is $120\,kV$. The maximum energy emitted by X-ray will be?
A. $1.2\times {{10}^{5}}\,eV$
B. ${{10}^{10}}\,eV$
C. ${{10}^{15}}\,eV$
D. ${{10}^{20}}\,eV$

Answer 1

Here first we will learn about Coolidge tube, who invented it, on what basis cathode and anti-cathode material are selected, and then solve the above problem using kinetic energy formula. The kinetic energy of any particle is the measure of its energy due its momentum.

Formula used:
The kinetic energy of a body is given by the formula,
$K.E = \dfrac{1}{2}m{v^2}$
where, $K.E$ is the kinetic energy of the body $m$ is the total mass of the body and $v$ is the velocity of the body.

Complete step by step answer:
X-ray has a wavelength of approximately 0.01 to 10 nm. It's a cutting-edge X-ray tube. The Coolidge tube is named after William D. Coolidge, a scientist. After the cold cathode tube, this tube was widely used.

This tube is also known as a hot cathode tube since electrons are emitted by thermionic emission, which occurs when the thermal energy provided to the carrier exceeds the material's work function. The hot cathode (negative) emits X-rays, which are accelerated by a potential difference V of several thousand volts (e.g. 50kV) The high-energy electrons collide with a copper anode's embedded target (positive).

Anti-cathode material selection: The majority of electrons strike the metal mark, but they only cause atoms to vibrate. As a result, the metal absorbs a great deal of energy and becomes heated. As a result, a metal with a high melting point is required. Because of the high atomic number, more X-rays are made.

Cathode content selection: Low heat power, low work function, and good heat conductor.
Here, potential difference between cathode and anti-cathode $=120\,kV$
The maximum energy of emitted X−rays will =?
$\Rightarrow \text{Maximum energy}= e \times V$
$\Rightarrow \text{Maximum energy}=120\times {{10}^{3}}\,eV$
$\therefore \text{Maximum energy}=1.2\times {{10}^{5}}\,eV$

Hence, the correct answer is option A.

Note: When fast moving, rapidly accelerated electrons collide with a target element with a high melting point and atomic number, coolidge tube X-rays are emitted. The kinetic energy of the electron is supplied by the voltage source hence the voltage or electrical energy is converted into kinetic energy between the terminals of the coolidge tube.