Lecture 20 Electromagnetic Waves

LECTURE 20 ELECTROMAGNETIC WAVES

25.6 The photon model of X"rays'are'used'in'CAT'scans. electromagnetic waves 25.7 The electromagnetic spectrum Radio waves and microwaves Infrared, visible light, and ultraviolet X rays and gamma rays 28.1X rays and x-ray diffraction X-ray images X-ray diffraction 25.6 The photon model of electromagnetic waves

! The photon model of electromagnetic waves: 1. Electromagnetic waves consist of discrete, massless units called photons. A photon travels in a vacuum at the speed of light. 2. Each photon has energy:

!"#$%$& = ℎ)

" ) is the frequency of the wave and ℎ = 6.63 × 10)*+ J - s = 4.14 × 10)01 eV - s is the Planck’s constant. 3. The superposition of a sufficiently large number of photons has the characteristics of a continuous electromagnetic wave. Quiz: 25.6-1

! A radio tower emits two 50 W signals, one an AM signal at a frequency of 850 kHz, one an FM signal at a frequency of 85 MHz. Which signal has more photons per second? A. The AM signal has more photons per second. B. The FM signal has more photons per second. C. Both signals have the same photons per second. Quiz: 25.6-1 answer

! A radio tower emits two 50 W signals, one an AM signal at a frequency of 850 kHz, one an FM signal at a frequency of 85 MHz. Which signal has more photons per second?

A. The AM signal has more photons per second.

#$%$&' )#*+%$%, )-. ! ! = = = ( ( ( ! The emission power of the radio tower is the same for both signals.

! The lower the frequency /, the greater the number of photons 0. Quiz: 25.6-2 (Knight P25.44)

! Rod cells in the retina of the eye detect light using a photopigment called rhodopsin. 1.8 eV is the lowest photon energy that can trigger a response in rhodopsin. What is the maximum wavelength of electromagnetic radiation in nm that can cause a transition? Quiz: 25.6-2 (Knight P25.44) answer

! !"#$%$&, ()& = ℎ,()&

-!"#$#%, '(% ! , = ()& ) 789 ? / )/ 2.42 × 46 :;<= >.6 × 46 +⁄= FG ! *+,- = = = = 6.9 × 10 m = 690 nm 0'(% 1!"#$#%, '(% 4.A:;

! Follow-up: In what part of the spectrum is this? Quiz: 25.6-2 (Knight P25.44) answer

! Follow-up: In what part of the spectrum is 690 nm? Visible deep red. And this is the upper end of the visible light spectrum for humans.

! For fun: A rod cell can respond to a single photon and is about 100 times more sensitive to a single photon than cones, so it is used for night vision.

Wavelength responsiveness of short (S), medium (M) and long (L) wavelength cones compared to that of rods (R). 25.7 The electromagnetic spectrum

! Radio waves are best described by Maxwell’s theory of electromagnetic waves because of their long wavelengths and low photon energies.

! Gamma rays and x rays are best described as photons because of their short wavelengths and high photon energies.

! Visible light, ultraviolet, and infrared can be described as waves or as photons, depending on the situation. 25.7 Radio waves and microwaves

! Radio waves and microwaves are generally produced by the motion of charges through an antenna.

! In an antenna, the oscillation of charges at a particular frequency ! causes the electric field to oscillate, which creates an induced magnetic field. A polarized electromagnetic wave of frequency ! radiates out into space. Quiz: 25.7-1

! The detection of radio waves can be accomplished with either a dipole antenna or a loop antenna. The dipole antenna detects the _____ field of the wave, and the loop antenna detects the _____ field of the wave. A. electric; electric B. electric; magnetic C. magnetic; magnetic D. magnetic; electric Quiz: 25.7-1 answer / Demo

! The dipole antenna detects the electric field of the wave, and the loop antenna detects the magnetic field of the wave. ! The electric field pushes the electrons in the dipole antenna, inducing a current in the antenna. The changing magnetic flux through the loop induces a current in the loop. ! The current induced in the antenna can be selectively amplified by the receiver. ! Demo: Cenco 3-meter Transmitter 25.7 Radio waves and microwaves

! In a microwave oven, microwaves exert a torque on water molecules, which has a large dipole moment.

! The molecules transfer the rotational energy to the thermal energy in the food in the microwave via molecular collisions. 25.7 Infrared, visible light, and ultraviolet

! The infrared, visible light, and ultraviolet portion of the electromagnetic spectrum is atomic radiation.

! Nearly all atomic radiation in our environment is thermal radiation.

! The peak wavelength of thermal radiation is given by Wien’s law:

2.9 × 100 nm 1 K ! in nm = "#$% 3 in K Quiz: 25.7-2

! A brass plate at room temperature (300 K) radiates power. What would happen if its temperature is raised to 600 K? Choose all that apply. A. The radiation power would increase. B. The radiation power would decrease. C. The radiation power would remain the same. D. The wavelength of maximum radiated intensity would increase. E. The wavelength of maximum radiated intensity would decrease. F. The wavelength of maximum radiated intensity would remain the same. Quiz: 25.7-2 answer

! A brass plate at room temperature (300 K) radiates power. What would happen if its temperature is raised to 600 K?

! The radiation power would increase.

! The wavelength of maximum radiated intensity would decrease.

! Making an object hotter causes it to emit more radiation across the entire spectrum, and lowers its peak *., × ./0 1234 wavelength: ! in nm = "#$% 5 61 4 Quiz: 25.7-3 (Knight P25.57)

! If astronomers look toward any point in outer space, they see radiation that matches the emission spectrum of an object at 2.7 K, a remnant of the Big Bang. What is the peak wavelength of this radiation in meters? Quiz: 25.7-3 (Knight P25.57) answer

! This is in microwave range, and called cosmic microwave background radiation.

For fun: Cosmic microwave background spectrum measured by the FIRAS instrument on the COBE, the most precisely measured black body spectrum in nature. Example: 25.7-1

! A python can detect thermal radiation with intensity greater than 0.60 W/m2. A typical mouse body has a surface area of 7.9 × 10'( m2, a surface temperature of 35 ℃, and an emissivity * = 0.97 at infrared wavelengths. What is the maximum distance from which a python can detect a mouse if the temperature of the environment is 20 ℃? You can model the mouse as a point source of radiation. 25.7 X rays and gamma rays & 28.1X rays and x-ray diffraction

! X rays are emitted by electrons and travel in straight lines like particles but can pass through solid materials.

! X-rays used in medical applications are produced by an x-ray tube in which energetic electrons collide with a metal target.

! Gamma rays are emitted in a nuclear process.

! X rays and gamma rays (and some ultraviolet rays) are ionizing radiation.

! When such radiation strikes tissue, the resulting ionization can produce cellular damage. 28.1 X-ray images

! An x-ray image is created when x rays are sent through a part of the body lying on film.

! The dense tissues pass few x rays, so the film is not exposed in those regions.

! In a computerized axial tomography (CAT) scan, thin beams of x-rays are directed through the body from a variety of directions, resulting in cross-sectional slice images or 3D images. 28.1 X-ray diffraction

! X-ray diffraction by crystalline lattice produces constructive interference pattern when the angle of incidence !" satisfies the Bragg condition:

∆$ = 2' cos !" = +, + = 1, 2, 3, ⋯

! X-ray diffraction patterns reveal details of structures that produce them. Quiz: 28.1-1

! In an x-ray diffraction experiment with a certain crystal for mono- energetic x-rays, the first order maximum is observed to be at 65º. What higher orders of maxima are possible with this crystal for these x-rays? Choose all that apply. A. None B. 2nd C. 3rd D. 4th E. 5th Quiz: 28.1-1 answer

! 2nd When x-rays scatter from a crystal the maxima are given by: ∆" = 2% cos )* = +,, + = 1, 2, 3, ⋯ 1 or cos ) = + , + = 1, 2, 3, … * 23 1 ! If + = 1, cos 65° = 0.42 = 23 1 ! For + = 2, cos ) = 2 = 2×0.42 = 0.84 2 23 1 ! But + = 3, cos ) = 3 = 3×0.42 = 1.26 which means = 23 it’s not possible since cos ) ≤ 1!