a) [tex]1.2\cdot 10^{-10} m[/tex]
The wavelength and the frequency of an electromagnetic wave are related by the wave equation:
[tex]c=f\lambda[/tex]
where
[tex]c=3.0\cdot 10^8 m/s[/tex] is the speed of light
f is the frequency of the wave
[tex]\lambda[/tex] is the wavelength
For the wave in this problem, the frequency is
[tex]f=2.5\cdot 10^{18} Hz[/tex]
So, we can re-arrange the equation to find their wavelength:
[tex]\lambda=\frac{c}{f}=\frac{3\cdot 10^8}{2.5\cdot 10^{18}}=1.2\cdot 10^{-10} m[/tex]
b) X-rays
The electromagnetic spectrum consists of the following types of waves, with the corresponding range of wavelength reported:
gamma rays < [tex]10^{-12} m[/tex]
x-rays [tex]10^{-9}-10^{-12}m[/tex]
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 [tex]1.2\cdot 10^{-10} m[/tex], 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).
