Radiation with a wavelength 4.2 nm?

To determine the nature of radiation with a wavelength of 4.2 nm, we can calculate its frequency and energy using the following equations:

Frequency (f) = Speed of light (c) / Wavelength (λ)

Energy (E) = Planck's constant (h) * Frequency (f)

Given the wavelength (λ) = 4.2 nm = 4.2 x 10^-9 meters:

1. Calculating the frequency (f):

c = 3 x 10^8 meters per second (speed of light)

f = c / λ = (3 x 10^8 m/s) / (4.2 x 10^-9 m) = 7.14 x 10^16 Hz

2. Calculating the energy (E):

h = 6.626 x 10^-34 Joules-seconds (Planck's constant)

E = h * f = (6.626 x 10^-34 J-s) * (7.14 x 10^16 Hz) = 4.74 x 10^-17 Joules

Based on these calculations, the radiation with a wavelength of 4.2 nm falls in the X-ray region of the electromagnetic spectrum. X-rays are characterized by their high energy and short wavelengths. They are commonly used in medical imaging, security screening, and industrial applications.