Download Modern Physics Mass-Energy Equivalence

Mass-Energy Equivalence
Modern Physics
• Mass and energy are related by what is
certainly the best-known equation in physics:
E  mc 2
• E is the energy equivalent (called mass
energy) of mass m, and c is the speed of light
(3 x 108 m/s)
Example 1. What is the energy equivalent of 1
kilogram of matter?
Example 2. The atomic bomb that exploded over
Hiroshima released 6.7 x 1013 J (67 TJ) of energy.
How much mass was converted to energy in this
explosion?
E = mc2
m = 1 kg
c = 3 x 108 m/s
E = mc2
E = 6.7 x 1013 J
c = 3 x 108 m/s
E = (I kg)(3 x 108)2
E = (I kg)(9 x 1016 m2/s2)
6.7 x 1013 J = m(3 x 108)2
6.7 x 1013 J = m(9 x 1016 m2/s2)
(6.7 x 1013)/(9 x 1016 ) = m
E = 9 x 1016 J
m = 7.44 x 10-4 kg = 0.744 g
Einstein’s Theory of Special Relativity
• The speed of light isn’t just a number… it is the
fundamental way that space and time are related, as
spacetime
• Gravity is a geometric property of spacetime
• Implies the existence of black holes
– Distortions of spacetime
– Not even light can escape
• Implies that, if you observe an object moving fast
enough (near c)…
– time appears to slows down
– length appears to stretch
The Dual Nature of Light
Is light a wave, or a particle? Or both?
• We already know that light can travel as a
wave & exhibits the following wave
behaviors:
–
–
–
–
–
Reflection
Refraction
Diffraction
Interference
Polarization
• This is known as the wave nature of light
• “[spacetime tells matter how to move; matter tells
spacetime how to curve]” – J.A. Wheeler
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The Dual Nature of Light
Is light a wave, or a particle? Or both?
• However… light can also travel in particle form
– Small bundles of light
– called photons
• Photons exhibit the following behaviors:
– Reflection
– Refraction
– Photoelectric effect
• This is known as the particle nature of light
APPLY: Which colors of light carry more energy? Which carry less energy?
APPLY: How do you know?
About Photons
• 1 photon = 1 quantum (fundamental unit) of
light.
• Photons move only at one speed…
– the speed of light, c
– c = 3 x 108 m/s (that’s like travelling around the
entire earth about 7.5 times in one second)
• According to Max Planck, the energy of a
photon is directly proportional to its frequency
– E = hf (E is measured in J, f is measured in Hz)
– h = Planck’s Constant, 6.63 x 10-34 J∙s
The Photoelectric Effect
• Photo = light (photons), electric = electrons
• When high-frequency light strikes certain
metals like potassium, the light is absorbed
and causes electrons to pop off
• The ejected electrons have an energy
proportional to the frequency of the light
• Watch it here
http://science.hq.nasa.gov/kids/imagers/ems/visible.ht ml
Spectra
The Photoelectric Effect: Proof of Particle Theory
• When the light source is brightened (higher
intensity)…
… more photons are produced, so…
… more electrons are ejected, but they do not have
more energy (they move at the same speed)
• With waves, brighter light means more energy
• Therefore… the photoelectric effect supports
the particle theory
• Spectroscopy: observing the dispersion of an
object's light into its component colors (i.e.
energies).
• Uses a spectroscope
• There are three basic types of spectra:
– Continuous
– Emission
– Absorption
http://csep10.phys.utk.edu/astr162/lect/light/absorption.html
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Continuous Spectrum
Emission Spectrum
• Comes from dense gases or solid objects
which radiate energy away through the
production of light.
• The emitted light has a broad range of
wavelengths, so the spectrum seems smooth
and continuous
• Examples: stars, incandescent light bulbs,
electric cooking stove burners, flames, cooling
fire embers… things that “glow”
• Emission Spectra are produced by thin gases
in which the atoms do not experience many
collisions (because of the low density).
• The emission lines correspond to photons that
are emitted when excited atomic states in the
gas make transitions back to lower-lying
levels.
• Basically, photons “pop off” excited atoms
with characteristic colors of light
Absorption Spectrum
Elements and Spectral Fingerprints
• When light passes through a cold, dilute gas,
atoms in the gas absorb light at characteristic
frequencies
• Dark lines (absence of light) in the spectrum
occur at the frequencies where the light is
absorbed
Nuclear Physics
Fission and Fusion
Nuclear energy is produced in two different
ways.
• Fission: Large nuclei are split to release
energy.
• Fusion: Small nuclei are combined to release
energy.
• Each element has a unique emission and
absorption spectrum
– acts as a “fingerprint”
– allows for identification of the element
• Let’s take a look http://jersey.uoregon.edu/elements/Element
s.html
Nuclear Fission
• Fission = splitting, causing energy to be released
• Examples:
– The atomic bomb
– Nuclear reactors
• Uranium is most often used in fission reactions
– Easily split by shooting neutrons at U nuclei
– Splitting results in three things:
• Daughter products – the “leftover” material (ex. Th-234, Pa-234, Pb-206 )
• Energy – used to heat water to make steam to turn a turbine
• Additional neutrons – which go on to cause more fission
– Since more neutrons are released, the reaction occurs over and
over… a chain reaction
– In reactors, excess neutrons are absorbed by control rods to
avoid overheating from chain reactions.
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Nuclear Reactors – Controlled
Chaos!
• Here, control rods are down
• Excess neutrons are
absorbed
• Reaction is “cool”
Nuclear Fusion
• Fusion = joining together, or fused.
• Only occurs under very hot conditions, like…
– The Sun (or any star)
– Hydrogen bombs
• Stars release heat and light through nuclear fusion
–
Hydrogen nuclei fuse to make helium, and later heavier
elements
• The hydrogen bomb works through fusion
– Humanity's most powerful and destructive weapon
– To start the reaction, we use an atomic bomb to generate
enough energy
– Hydrogen nuclei fuse to form helium and in the process
release huge amounts of energy, which creates a huge
explosion
• Here, control rods are up
• Excess neutrons continue to
cause more reactions
• Reaction is “hot”
Nuclear Stability
• Not all nuclei are given to reaction.
– Stable nuclei are not radioactive
– Unstable nuclei have the tendency of emitting
some kind of radiation (they are radioactive)
• The neutron to proton (n/p) ratio is the
dominant factor in nuclear stability
– For low atomic numbers, stability occurs at a ratio
very close to 1
– As atomic number increases, the ratio increases
– The heaviest stable isotope is Bi-209 (n/p = 1.518)
Types of Radiation Particles
• Alpha Particle: α2+, or He2+
– Consists of 2 protons & 2 neutrons
– Looks similar to a helium atom
– Heavy and large, stopped by paper
• Beta Particle: β+ or β– β+ is a positron, β+ is an electron
– Can be stopped by a sheet of aluminum foil
• Gamma Radiation: γ
– Basically, very high-frequency EM radiation (photons)
– Biologically hazardous, can only be stopped by thick
lead
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Why only three types of decay?
• It has to do with two of the four fundamental
forces: strong nuclear & weak nuclear
• Strong Nuclear
– Holds the nucleus (p+ and n0) together
– Holds quarks together to form p+ and n0 g
– Allows alpha decay due to the stable nature and
low mass of the alpha particle
• Weak Nuclear
– Holds atoms (electrons and nuclei) together
– Responsible for beta decay
Applications of Modern Physics
• Radiation Therapy –
– high-energy radiation from many sources, such as…
• X-rays
• gamma rays
• fast-moving subatomic particles (particle or, proton beam, therapy)
– used to kill cancer cells and shrink tumors
• Diagnostic imaging –
– Technologies to look inside the body for clues about a medical
condition
– X-rays, CT scans, MRI scans, PET scans, Nuclear scans
More on Diagnostic Imaging
• X-ray: uses electromagnetic radiation to make
images
• Computed tomography (CT): uses specialized X-ray
equipment to create cross-sectional pictures of a
body
• Magnetic Resonance Imaging (MRI): uses a large
magnet and radio waves to look at organs and soft
structures inside the body
• Positron Emission Tomography (PET): uses positronemitting isotopes to make 3D images of internal
structures
• Nuclear scanning: uses radioactive substances
(tracers) to see structures and functions inside your
body
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