Having read a number of books on cosmology and particle physics, I found my-self raking through 5 or 6 books or looking on the web as I tried to remember some tangible fact that had interested me. In the end, I decided to gather this info and post it under various headings as blogs on MySpace. With the introduction of LaTeX at Physics Forums, I decided to move a couple of them over here. Some are a year old, some are more recent. MySpace blogs
Mass-energy Conversion
Conversion of mass into energy
e = mc^2*
where e is energy in joules (watts/second), m is mass in kg and c is the speed of light in metres/second (299,792,458 m/s)
*The full equation is e^2 = (pc)^2 + m^2c^4 where in the case of photons, p = h/[itex]\lambda[/itex], where h is Planck's constant and [itex]\lambda[/itex] is the photons wavelength (see bottom of page).
Based on the above calculation, 1 gram of matter would produce the following-
e = 0.001 x 299,792,458^2 = 0.001 x 9x10^16 = 9x10^13 joules or 90,000 Gigajoules (this relies on absolute annihilation of the matter).
Protons and neutrons within atomic nuclei are held together with a binding energy called the strong force. Of the 4 fundamental forces in the Universe (gravity, the weak force, electromagnetism and strong force) the strong force is 10^38 times stronger than gravity. It is this binding energy that is released during mass to energy conversions. The force that binds protons and neutrons is actually called the residual stong force (or nucleon force) as it is a result of the strong force that binds quarks within the protons and neutrons.
2 methods of tapping into this energy are- nuclear fission (splitting uranium-235) and nuclear fusion (fusing deuterium and tritium, 2 hydrogen isotopes).
With a fission reactor, rods of uranium are bombarded with neutrons, which collide with the already overripe nucleus of the uranium-235 atom (92 protons, 143 neutrons) causing it to split (one such reaction is to split into lanthanum-148 (57 protons, 91 neutrons) and bromine-85 (35 protons, 50 neutrons) plus 3 neutrons which continue the fission process with other nuclei). The resulting divided elements together weight slightly less (due to less binding energy being required) than the original uranium-235 atom by about 0.15% and it is this difference in mass that is turned into energy. The rods are suspended in a tank of heavy water, which disrupts the path of the neutrons, helping them collide with the uranium nuclei. Heavy water is also known as deuterium oxide and consists of the heavier hydrogen isotope deuterium (1 proton, 1 neutron) as apposed to the single proton of hydrogen mixed with oxygen. Rods of boron, which soak up neutrons, are raised/lowered into the reactor to control the reactions (without these, the reactor would be akin to a nuclear bomb).
Fusion reactors are still in the experimental phase, these normally consist of a Tokamak (torodial chamber in magnetic coils), which contain deuterium (1 proton, 1 neutron) and tritium (1 proton, 2 neutrons) heated to a plasma contained in a magnetic field. The deuterium and tritium are fused to create helium (2 protons, 2 neutrons) plus 1 extra neutron (the helium and extra neutron have less mass than the original deuterium and tritium and the difference in mass becomes energy). The extra neutron carries 80% of the the energy through the magnetic field (as it has no charge) and into a lithium 'blanket' which surrounds the Tokamak. Here, the neutron reacts with the lithium, creating more tritium, and the energy from the fast neutron is absorbed by the blanket passing into piped water which then drive steam generated turbines to create electricity.
Fusion takes place in the Sun as a result of massive gravitational pressure and temperatures of 10 to 15 million degrees in the core. We don't have the benefits of gravitational pressure on Earth to induce fusion so the temperatures within the Tokamak have to be 10 times that of the Sun (100-150 million degrees). The biggest problem scientists have faced is creating a magnetic field that can contain the plasma (this has been compared to trying to hold jelly together with a series of elastic bands). The JET (Joint European Torus) experimental fusion reactor had a production ratio of 0.7 (energy out/energy in) not including the energy used for confinement. This is expected to rise to about 10 for the ITER (Internationa Thermonuclear Experimental Reactor) reactor and 25-30 for commercial reactors such as DEMO (DEMOnstration Power Plant).
View inside the JET experimental fusion reactor-
Though fusion produces less energy per reaction, it produces more energy per mass. A uranium reaction produces 200 MeV* per uranium-235 atomic mass, giving an output of 0.85 MeV (200 divided by 235) for every amu (atomic mass unit). A deutirium-tridium reaction produces 17.6 MeV, giving an output of 3.52 MeV (17.6 divided by 5) for every amu. The fusion of D-T converts approx. 4 times more mass into energy than the fission of uranium-235. Only about 0.15% of the uranium mass is converted into energy during fission while approx. 0.6% of the deuterium/tritium mix is converted into energy through fusion.
Based on the above, 100g of uranium would release 14,400 Gj of energy (a gigajoule being a billion joules) through fission. 100g of deuterium-tritium mix would produce 57,600 Gj of energy through fusion.
*An electron volt (eV) is used as the measurement of electrical charge at the quantum level. It is equivalent to the amount of kinetic energy gained by a single unbound electron when it passes through an electrostatic potential difference of one volt in a vacuum. Basically it equals 1.60217653x10^-19 joules. A photon is 0.938 GeV, the electron is 0.511 MeV. The resulting energy released from an electron/positron (the antimatter of an electron) reaction is the sum of the 2 parts- 0.511 MeV x 2 = 1.022 MeV. Because of e = mc^2 the actual weight of these small particles can be calculated from the energy they produce, 0.511 MeV/c^2 = mass.
Recommended reading- 'Fusion: Energy of the Universe' by Garry McCracken and Peter Stott.
Photons
The full equation for Einstein’s famous equation is e^2 = (pc)^2 + m^2 c^4. The first part (e = pc) relates to objects of very little or no mass at ultra-relativistic speeds and the second part (e = mc^2) relates to objects of mass at rest. Where momentum (p) normally equals mv (mass x velocity), in the case of a photon, p = h/[itex]\lambda[/itex], where h is Planck's constant and lambda is the photons wavelength, therefore e = hc/[itex]\lambda[/itex] (or e = hf where f = c/[itex]\lambda[/itex]) and the photon has no mass. In the case of a photon at your average visible wavelength (say green with a wavelength of 550 nm, or 0.55x10^-6 m), the energy for that photon is 3.61x10^-19 joules, for gamma rays (with a wavelength of 5 pm (picometres) or 5x10^-12 m), the energy is 3.97x10^-14 joules per photon, some 100,000 times more energized than visible light. When we talk of a photon loosing some of it’s energy (say when striking a wall) what happens is that some of the photons energy is transfered to the medium it comes in contact with and as a consequence, it’s frequency is reduced (i.e., its wavelength is increased).
e = mc^2*
where e is energy in joules (watts/second), m is mass in kg and c is the speed of light in metres/second (299,792,458 m/s)
*The full equation is e^2 = (pc)^2 + m^2c^4 where in the case of photons, p = h/[itex]\lambda[/itex], where h is Planck's constant and [itex]\lambda[/itex] is the photons wavelength (see bottom of page).
Based on the above calculation, 1 gram of matter would produce the following-
e = 0.001 x 299,792,458^2 = 0.001 x 9x10^16 = 9x10^13 joules or 90,000 Gigajoules (this relies on absolute annihilation of the matter).
Protons and neutrons within atomic nuclei are held together with a binding energy called the strong force. Of the 4 fundamental forces in the Universe (gravity, the weak force, electromagnetism and strong force) the strong force is 10^38 times stronger than gravity. It is this binding energy that is released during mass to energy conversions. The force that binds protons and neutrons is actually called the residual stong force (or nucleon force) as it is a result of the strong force that binds quarks within the protons and neutrons.
2 methods of tapping into this energy are- nuclear fission (splitting uranium-235) and nuclear fusion (fusing deuterium and tritium, 2 hydrogen isotopes).
With a fission reactor, rods of uranium are bombarded with neutrons, which collide with the already overripe nucleus of the uranium-235 atom (92 protons, 143 neutrons) causing it to split (one such reaction is to split into lanthanum-148 (57 protons, 91 neutrons) and bromine-85 (35 protons, 50 neutrons) plus 3 neutrons which continue the fission process with other nuclei). The resulting divided elements together weight slightly less (due to less binding energy being required) than the original uranium-235 atom by about 0.15% and it is this difference in mass that is turned into energy. The rods are suspended in a tank of heavy water, which disrupts the path of the neutrons, helping them collide with the uranium nuclei. Heavy water is also known as deuterium oxide and consists of the heavier hydrogen isotope deuterium (1 proton, 1 neutron) as apposed to the single proton of hydrogen mixed with oxygen. Rods of boron, which soak up neutrons, are raised/lowered into the reactor to control the reactions (without these, the reactor would be akin to a nuclear bomb).
Fusion reactors are still in the experimental phase, these normally consist of a Tokamak (torodial chamber in magnetic coils), which contain deuterium (1 proton, 1 neutron) and tritium (1 proton, 2 neutrons) heated to a plasma contained in a magnetic field. The deuterium and tritium are fused to create helium (2 protons, 2 neutrons) plus 1 extra neutron (the helium and extra neutron have less mass than the original deuterium and tritium and the difference in mass becomes energy). The extra neutron carries 80% of the the energy through the magnetic field (as it has no charge) and into a lithium 'blanket' which surrounds the Tokamak. Here, the neutron reacts with the lithium, creating more tritium, and the energy from the fast neutron is absorbed by the blanket passing into piped water which then drive steam generated turbines to create electricity.
Fusion takes place in the Sun as a result of massive gravitational pressure and temperatures of 10 to 15 million degrees in the core. We don't have the benefits of gravitational pressure on Earth to induce fusion so the temperatures within the Tokamak have to be 10 times that of the Sun (100-150 million degrees). The biggest problem scientists have faced is creating a magnetic field that can contain the plasma (this has been compared to trying to hold jelly together with a series of elastic bands). The JET (Joint European Torus) experimental fusion reactor had a production ratio of 0.7 (energy out/energy in) not including the energy used for confinement. This is expected to rise to about 10 for the ITER (Internationa Thermonuclear Experimental Reactor) reactor and 25-30 for commercial reactors such as DEMO (DEMOnstration Power Plant).
View inside the JET experimental fusion reactor-
Though fusion produces less energy per reaction, it produces more energy per mass. A uranium reaction produces 200 MeV* per uranium-235 atomic mass, giving an output of 0.85 MeV (200 divided by 235) for every amu (atomic mass unit). A deutirium-tridium reaction produces 17.6 MeV, giving an output of 3.52 MeV (17.6 divided by 5) for every amu. The fusion of D-T converts approx. 4 times more mass into energy than the fission of uranium-235. Only about 0.15% of the uranium mass is converted into energy during fission while approx. 0.6% of the deuterium/tritium mix is converted into energy through fusion.
Based on the above, 100g of uranium would release 14,400 Gj of energy (a gigajoule being a billion joules) through fission. 100g of deuterium-tritium mix would produce 57,600 Gj of energy through fusion.
*An electron volt (eV) is used as the measurement of electrical charge at the quantum level. It is equivalent to the amount of kinetic energy gained by a single unbound electron when it passes through an electrostatic potential difference of one volt in a vacuum. Basically it equals 1.60217653x10^-19 joules. A photon is 0.938 GeV, the electron is 0.511 MeV. The resulting energy released from an electron/positron (the antimatter of an electron) reaction is the sum of the 2 parts- 0.511 MeV x 2 = 1.022 MeV. Because of e = mc^2 the actual weight of these small particles can be calculated from the energy they produce, 0.511 MeV/c^2 = mass.
Recommended reading- 'Fusion: Energy of the Universe' by Garry McCracken and Peter Stott.
Photons
The full equation for Einstein’s famous equation is e^2 = (pc)^2 + m^2 c^4. The first part (e = pc) relates to objects of very little or no mass at ultra-relativistic speeds and the second part (e = mc^2) relates to objects of mass at rest. Where momentum (p) normally equals mv (mass x velocity), in the case of a photon, p = h/[itex]\lambda[/itex], where h is Planck's constant and lambda is the photons wavelength, therefore e = hc/[itex]\lambda[/itex] (or e = hf where f = c/[itex]\lambda[/itex]) and the photon has no mass. In the case of a photon at your average visible wavelength (say green with a wavelength of 550 nm, or 0.55x10^-6 m), the energy for that photon is 3.61x10^-19 joules, for gamma rays (with a wavelength of 5 pm (picometres) or 5x10^-12 m), the energy is 3.97x10^-14 joules per photon, some 100,000 times more energized than visible light. When we talk of a photon loosing some of it’s energy (say when striking a wall) what happens is that some of the photons energy is transfered to the medium it comes in contact with and as a consequence, it’s frequency is reduced (i.e., its wavelength is increased).
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