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Chapter 22: Problem 22

In order to study the structure of a crystalline solid, you want to illuminate it with EM radiation whose wavelength is the same as the spacing of the atoms in the crystal \((0.20 \mathrm{nm}) .\) (a) What is the frequency of the EM radiation? (b) In what part of the EM spectrum (radio, visible, etc. \()\) does it lie?

Short Answer

Expert verified
Answer: The frequency of the EM radiation is 1.5 x 10^18 Hz, and it belongs to the X-ray part of the electromagnetic spectrum.

Step by step solution

01

Calculate the frequency ν of the EM radiation

To find the frequency, we will use the formula connecting wavelength and frequency for EM waves: wavelength λ = speed of light c / frequency ν Rearrange the formula to solve for the frequency: ν=c/λ The speed of light c is approximately 3.0 x 10^8 m/s, and the given wavelength λ is 0.20 nm or (0.20 x 10^-9 m). Substitute these values into the formula and solve for the frequency: ν=(3.0 x 10^8 m/s)/(0.20 x 10^-9 m) ν = 1.5 x 10^18 Hz
02

Identify the part of the EM spectrum the radiation lies in

Now that we have the frequency, we can determine which part of the EM spectrum the radiation belongs to. Here's a list of ranges in the EM spectrum: - Radio waves: Below 3 x 10^11 Hz - Microwaves: 3 x 10^11 to 3 x 10^12 Hz - Infrared: 3 x 10^12 to 4.3 x 10^14 Hz - Visible light: 4.3 x 10^14 to 7.5 x 10^14 Hz - Ultraviolet: 7.5 x 10^14 to 3 x 10^17 Hz - X-rays: 3 x 10^17 to 3 x 10^19 Hz - Gamma rays: Above 3 x 10^19 Hz Since the frequency we calculated (1.5 x 10^18 Hz) falls in the range for X-rays, the EM radiation lies in the X-ray part of the spectrum. To summarize: a) The frequency of the EM radiation is 1.5 x 10^18 Hz. b) The EM radiation lies in the X-ray part of the electromagnetic spectrum.

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