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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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Most popular questions from this chapter

In musical acoustics, a frequency ratio of 2: 1 is called an octave. Humans with extremely good hearing can hear sounds ranging from \(20 \mathrm{Hz}\) to \(20 \mathrm{kHz}\), which is approximately 10 octaves (since $2^{10}=1024 \approx 1000$ ). (a) Approximately how many octaves of visible light are humans able to perceive? (b) Approximately how many octaves wide is the microwave region?
A microwave oven can heat 350 g of water from \(25.0^{\circ} \mathrm{C}\) to \(100.0^{\circ} \mathrm{C}\) in 2.00 min. (a) At what rate is energy absorbed by the water? (b) Microwaves pass through a waveguide of cross-sectional area \(88.0 \mathrm{cm}^{2} .\) What is the average intensity of the microwaves in the wave guide? (c) What are the rms electric and magnetic fields inside the wave guide?
The magnetic field of an EM wave is given by \(B_{y}=\) $B_{\mathrm{m}} \sin (k z+\omega t), B_{x}=0,\( and \)B_{z}=0 .$ (a) In what direction is this wave traveling? (b) Write expressions for the components of the electric field of this wave.
The magnetic field in a radio wave traveling through air has amplitude $2.5 \times 10^{-11} \mathrm{T}\( and frequency \)3.0 \mathrm{MHz}$. (a) Find the amplitude and frequency of the electric field. (b) The wave is traveling in the \(-y\) -direction. At \(y=0\) and \(t=0\), the magnetic field is $1.5 \times 10^{-11} \mathrm{T}\( in the \)+z$ -direction. What are the magnitude and direction of the electric field at \(y=0\) and \(t=0 ?\)
The antenna on a cordless phone radiates microwaves at a frequency of $2.0 \mathrm{GHz}$. What is the maximum length of the antenna if it is not to exceed half of a wavelength?
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