Modern Physics

Mass-Energy Equivalence

• Mass and energy are related by what is certainly the best-known equation in physics:

• E is the energy equivalent (called mass energy) of mass m, and c is the speed of light (3 x 108 m/s)

2mcE

Example 1. What is the energy equivalent of 1 kilogram of matter?

E = mc2

m = 1 kgc = 3 x 108 m/s

E = (I kg)(3 x 108)2

E = (I kg)(9 x 1016 m2/s2)

E = 9 x 1016 J

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

E = 6.7 x 1013 J c = 3 x 108 m/s

6.7 x 1013 J = m(3 x 108)2

6.7 x 1013 J = m(9 x 1016 m2/s2)

m = 7.44 x 10-4 kg = 0.744 g

(6.7 x 1013)/(9 x 1016 ) = m

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

• “[spacetime tells matter how to move; matter tells spacetime how to curve]” – J.A. Wheeler

Nuclear PhysicsFission 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.

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.

Nuclear Reactors – Controlled Chaos!

• Here, control rods are down• Excess neutrons are

absorbed• Reaction is “cool”

• Here, control rods are up• Excess neutrons continue to

cause more reactions• Reaction is “hot”

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

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

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 positron-emitting isotopes to make 3D images of internal structures

• Nuclear scanning: uses radioactive substances (tracers) to see structures and functions inside your body

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

• 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

The Dual Nature of Light Is light a wave, or a particle? Or both?

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∙

http://science.hq.nasa.gov/kids/imagers/ems/visible.html

APPLY: Which colors of light carry more energy? Which carry less energy?APPLY: How do you know?

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

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

Spectra • 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

Continuous 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 Spectrum

• 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

• 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

Elements and Spectral Fingerprints

• 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/Elements.html