Question

The MRI (magnetic resonance imaging) body scanners used in hospitals operate with 400 MHz radio frequency. The wavelength corresponding to this radio frequency is
(a) 0.75 m
(b) 0.75 cm
(c) 1.5 m
(d) 2 cm

Answer 1

Hint: MRI is a technique that uses radio waves and magnetic fields to obtain a detailed image of the physiology and anatomy of the body to identify any abnormality. As the waves used are electromagnetic waves, therefore the speed of the waves is equal to c (speed of light).

Formula used: The relation between c,v and \[\lambda \] is, \[c = v\lambda \]. Here, c stands for speed of light whose value is \[3 \times {10^8}m/s\] , v stands for frequency and \[\lambda \] stands for wavelength.

Complete Step by Step Answer:
Using the above relation of c, we have to find out the wavelength of the electromagnetic wave used in an MRI.
The given value of frequency is 400 MHz = \[400 \times {10^6}{\rm{Hz}} = 400 \times {10^6}{{\rm{s}}^{ - 1}}\]
On rearranging the equation of c, we get,
\[\lambda = \dfrac{c}{v}\]
On putting the values of c and v, we get,
\[\lambda = \dfrac{{3 \times {{10}^8}{\rm{m}}{s^{ - 1}}}}{{400 \times {{10}^6}{{\rm{s}}^{ - 1}}}} = 0.75\,{\rm{m}}\]
Therefore, the wavelength of the electromagnetic waves used in an MRI is 0.75 metres.
Hence, option a is right.

Note: The technique of MRI is better than other techniques such as CT scan or X-ray to diagnose any injury of the body. In MRI scans, no powerful ionising radiations are used. Therefore, it has more safety than CT scans or X-rays. Mostly MRI scanning is done for the spinal cord and brain to detect any abnormality. Its use in the detection of breast cancer, cysts, etc is significant. It is also helpful to evaluate any kind of heart problem.