Question

Hi, I need help with this problem, I don't understand how to solve it

Experiments are carried out in a laboratory in which particles that produce electromagnetic waves of 2.5χ
10¹⁸ HZ are accelerated.

Calculate:

a) What is its wavelength? (speed of light equal to 3χ 10⁸m / s)

b) What type of electromagnetic wave does it correspond to?

c) Is it safe to be exposed to this type of electromagnetic wave?

Answer 1

a)
`1.2\cdot 10^(-10) m`

The wavelength and the frequency of an electromagnetic wave are related by the wave equation:

`c=f\lambda`

where

`c=3.0\cdot 10^8 m/s` is the speed of light

f is the frequency of the wave

`\lambda` is the wavelength

For the wave in this problem, the frequency is

`f=2.5\cdot 10^(18) Hz`

So, we can re-arrange the equation to find their wavelength:

`\lambda=(c)/(f)=(3\cdot 10^8)/(2.5\cdot 10^(18))=1.2\cdot 10^(-10) m`

b) X-rays

The electromagnetic spectrum consists of the following types of waves, with the corresponding range of wavelength reported:

gamma rays <
`10^(-12) m`

x-rays
`10^(-9)-10^(-12)m`

ultraviolet 400 nm - 1 nm

visible 750 nm - 400 nm

infrared 25 μm - 750 nm

microwaves 1 mm - 25 μm

radio waves > 1 mm

The wavelength of the waves in this experiment is
`1.2\cdot 10^(-10) m`, so it falls in the x-rays range.

c) Only for a very short time

X-rays are very high energy electromagnetic waves, the second most energetic in the electromagnetic spectrum, just below gamma rays.

Gamma rays can be very dangerous: in fact, their penetrating power is very high, and since their energy is very high, they can penetrate the skin and release a lot of energy, causing potential damage to the cells (killing cells or causing cancer).

X-rays are also very penetrating, so they can penetrate through the skin, however their energy is less than that of gamma rays, so they can cause less damage. However, a prolonged dose can be equally dangerous, so the time of exposition to X-rays must be limited and kept as short as possible. X-rays are used in medicine, for example to produce x-rays images of bones or teeth: this is an example showing that the time of exposure must be kept short (in fact, the radiography generally lasts short, so the patient is exposed to the x-rays only for a limited time).