Question

An X-ray tube is operated at 1.24 million volts. Then find the shortest wavelength of the photon produced.
A. \[{10^{ - 2}}nm\]
B. \[{10^{ - 3}}nm\]
C. \[{10^{ - 4}}nm\]
D. \[{10^{ - 1}}nm\]

Answer 1

Hint: Wavelength is the distance between corresponding points of two consecutive waves. It is a defining characteristic of a wave and it depends on the medium in which it is traveling.

Formula Used:
The formula to find the minimum wavelength is,
\[{\lambda _{\min }} = \dfrac{{1240}}{{\Delta v}}\]
Where, \[\Delta v\] is potential difference or voltage.

Complete step by step solution:
Consider an X-ray tube that is operated at 1.24 million volts. Then we need to find the shortest wavelength of the photon. By the formula, we can write,
\[{\lambda _{\min }} = \dfrac{{1240}}{{1.24 \times {{10}^6}}}\] in nm
Here, given that, \[\Delta v = 1.24 \times {10^6}V\]

Now, substitute the value of\[\Delta v\]in the above equation, we get
\[{\lambda _{\min }} = \dfrac{{1240}}{{1.24 \times {{10}^6}}}\]
\[\therefore {\lambda _{\min }} = {10^{ - 3}}nm\]
Therefore, the minimum value of wavelength is \[{10^{ - 3}}\,nm\].

Hence, option B is the correct answer.

Additional information: A sound wave is a disturbance caused by the movement of energy traveling through a medium, such as water, air, or any other liquid or solid medium, as this sound wave propagates away from the source of the sound. There are two types of waves one is transverse wave and longitudinal wave. A water wave is an example of a wave that involves a combination of a longitudinal and transverse wave and sound waves are examples of longitudinal waves.

Note:Wavelength is the distance between two crests or two troughs of the wave. The wave changes its shape as it moves from one medium to another medium and the wavelength also changes. But the frequency does not change when the wave travels from one medium to another, that is it remains constant.