Hi, i need 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?

a)

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

where

is the speed of light

f is the frequency of the wave

is the wavelength

For the wave in this problem, the frequency is

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

b) X-rays

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

gamma rays<

x-rays

ultraviolet400 nm - 1 nm

visible750 nm - 400 nm

infrared25 μm - 750 nm

microwaves1 mm - 25 μm

radio waves> 1 mm

The wavelength of the waves in this experiment is , 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).

mistakes are ok