Question

To detect details of the size of atoms (about 1x10^(-10) m) with electromagnetic radiation, what frequency should the radiation have?

a) 3.0 × 10¹⁸ Hz
b) 3.0 × 10⁸ Hz
c) 3.0 × 10²⁸ Hz
d) 3.0 × 10³⁸ Hz

Answer 1

The frequency of electromagnetic radiation needed to detect details of the size of atoms is 3.0 × 1018 Hz, which corresponds to gamma rays. The correct option is a).

Step-by-step explanation:

To detect details of the size of atoms, which are about 1x10-10 m, we need electromagnetic radiation that has a wavelength of the same order of magnitude. The relationship between the frequency (f), wavelength (λ), and the speed of light (c) is given by c = fλ. Since the speed of light is a constant at approximately 3x108 m/s, we can calculate the required frequency to be:

f = c / λ
f = (3x108 m/s) / (1x10-10 m)
f = 3x1018 Hz

This frequency corresponds to gamma rays, which are at the high-frequency end of the electromagnetic spectrum and are capable of probing such small structures due to their short wavelengths. The mention of the correct option in the final part of the question would be (a) 3.0 × 1018 Hz.