chapter 16.2; mass, energy, and the theory of relativity

equation of the equivalence between matter and energy

E=mc²

• E stands for energy

• m stands for mass

  • mass is a measure of the quantity of matter

• c is a constant that relates the 2, the speed of light (3 × 10⁸ m/s)

• matter can be converted into energy, and energy can be converted into matter

• complete conversion of 1 gram of matter (approximately 1 paperclip) would produce as much energy as the burning of 15,000 barrels of oil

• allows us to calculate that the amount of energy radiated by the Sun could be produced by the complete conversion of about 4 million tons of matter into energy inside the Sun each second

antiparticle

for each kind of particle that exists, there is a corresponding antiparticle

• if the particle carries a charge, the antiparticle has the opposite charge

positron

antielectron

• has the same mass as the electron but is positively charged

antiproton

has a negative charge

antimatter

when a particle comes into contact with its antiparticle, the original particles are annihilated, and substantial amounts of energy in the form of photons are produced

• Since our world is made exclusively of ordinary particles of matter, antimatter cannot survive for very long

• individual antiparticles are found in cosmic rays (particles that arrive at the top of Earth’s atmosphere from space)

• individual antiparticles can be created in particle accelerators

neutrino

• type of elementary particle

• energy seemed to disappear when certain types of nuclear reactions took place, violating the law of conservation of energy

• physicist Wolfgang Pauli suggest that neutrinos were particles with zero mass, and that like photons, they moved with the speed of light

• detected in 1956

  • The reason it was so hard to find is that neutrinos interact very weakly with other matter and therefore are very difficult to detect

• most neutrinos can pass completely through a star or planet without being absorbed

• 3 different types

• 500000 times smaller than electrons

atomic nucleus

• inside, particles are held together by the strong nuclear force

  • short range force, only capable of acting over distances about the size of an atomic nucleus

  • an attractive force

  • if particles come together under the strong nuclear force and unite to form an atomic nucleus, some of the nuclear energy is released

  • the energy given up in such process is called the binding energy of the nucleus

binding energy of the nucleus

the energy given up/released when particles come together under the strong nuclear force in the nucleus and unite to form an atomic nucleus

• the resulting nucleus has slightly less mass than the sum of the masses of the particles that come together to form it

  • energy comes from the loss of mass, loss of mass is only a small fraction of the mass of 1 proton

binding energy for different atoms

• binding energy is greatest for atoms with a mass near that of the iron nucleus (protons + neutrons=56), less for atoms with both heavier and lighter nuclei

  • therefore Iron is the most stable element, since it gives up the most energy when it forms, it requires the most energy to break it back down to its component particles

nuclear fusion

• when light atomic nuclei come together to form a heavier one (up to iron), mass is lost and energy is released

nuclear fission

• when energy is produced by breaking up heavy atomic nuclei into lighter ones (down to iron)

• sometimes occurs spontaneously in some unstable nuclei through the process of natural radioactivity

how can nuclei come together close enough to participate in fusion?

• if we get protons close enough together within ‘striking distance’ of the nuclear force, they will come together with a much stronger attraction

• two protons can fuse only in regions with a temperature of over 12 million K, the speed of the protons average around 1000km/s or more

• On average, a proton will rebound from other protons in the Sun’s crowded core for about 14 billion years, at the rate of 100 million collisions per second, before it fuses with a second proton

nuclear reactions in the sun’s interior

• three step process that occurs inside the Sun that takes 4 hydrogen nuclei and fuses them together to form a single helium nucleus

• the helium nucleus is slightly less massive than the four hydrogen nuclei that combine to form it, and that mass is converted into energy

initial step to form a helium nucleus from four hydrogen nuclei

• high tempers, two protons combine to make a deuterium nucleus, which is an isotope of hydrogen that contains one proton and one neutron

  • of the the original protons has been converted into a neutron in the fusion reaction

• electric charge has to be conserved in nuclear reactions, and it is conserved in this one

  • a positron emerges from the reaction and carries away the positive charge originally associated with one of the protons

  • since its antimatter, the positron will collide with a nearby electron, both will be annihilated, producing electromagnetic energy in the form of gamma-ray protons

  • this gamma ray collides with particles of matter and transfers its energy to one of them

  • the particle later releases another gamma-ray photon, but often the mitted photon has a bit less energy than the one that was absorbed

  • by the time they reach the surface, gamma-ray photons are converted into separate lower-energy photons of sunlight

• neutrino also emitted, which travel directly to the Sun’s surface than out into space

  • move at speed of light, so they escape the Sun about 2 seconds after being created

• can take 100,000 - 1,000,000 years for the emission of energy to reach the surface of the Sun from the core

second step to form a helium nucleus from four hydrogen nuclei

• add another proton to the deuterium nucleus to create a helium nucleus that contains two protons and one neutron

• some mass is lost, more gamma radiated emitted

• called helium-3

thirds step to form a helium nucleus from four hydrogen nuclei

• helium-3 must combine with another helium-3 to form helium-4

• two energetic protons left over from this step, which come out of the reaction to collide with other protons to stars the 3 steps again

proton-proton chain

• first step: takes a long time

• second step: happens after 6 seconds

• third step: a million years after

• protons collide directly with other protons to form helium nuclei

CNO cycle (carbon-nitrogen-oxygen)

• occurs in hotter stars than the Sun