Saturday, December 31, 2011

EQUIVALENCE OF MASS AND ENERGY

      Einstein put forward new ideas regarding the relationship between space, time, mass and energy which have come to be known as the the theory of relativity . See post Einstein’s Achievements ( Part :2 ) . It had long been accepted that matter could not be destroyed. This assumbtion was expressed in the law of conservation of matter, which states that
the total quantity of matter in the universe is fixed and cannot be increased or decreased by human agency. Similarly, another law, called the law of conservation of energy, states that
the total quantity of energy in the universe is also constant and can be neither created nor destroyed.








      Einstein has simplified our picture of the universe by showing that
the mass of a body is a measure of the quantity of energy contained in it. We find that, in a nuclear reactor, the sum total of the masses of the atoms produced as a result of fission is slightly less than the mass of the original uranium nuclei. The difference represents the mass of the energy liberated as heat, radiation and kinetic energy of fission products. Thus, in the light of modern physics, we have to consider the laws of conservation of energy and mass as seperate aspects of a single principle. We now take the veiw that the sum total of mass plus energy in the universe is fixed
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          To understand the equivalence of mass and energy, consider the following thought experiment proposed by Einstein in developing his famous equation E = m c².

Imagine an isolated box of mass Mbox and length L initially at rest, as shown in Figure a. Suppose that a pulse of light is emitted from the left side of the box, as depicted in Figure b.
We know that light of energy E carries linear momentum  P = E / c . Hence, if momentum is to be conserved, the box must recoil to the left with a speed v. If it is assumed that the box is very massive, the recoil speed is much less than the speed of light, and conservation of momentum gives
v = E / MBox
The time it takes the light pulse to move the length of the box is approximately Δ t = L / c. In this time interval, the box moves a small distance  Δ x to the left,
        Δ x= v Δ t = El / MBox c²
The light then strikes the right end of the box and transfers its momentum to the box, causing the box to stop. With the box in its new position, its center of mass appears to have moved to the left. However, its center of mass cannot have moved because the box is an isolated system. Einstein resolved this puzzling situation
by assuming that in addition to energy and momentum, light also carries mass. If Mpulse is the effective mass carried by the pulse of light and if the center of mass of the system (box plus pulse of light) is to remain fixed, then
        Mpulse × L = Mbox × Δ x
Solving for Mpulse , and using the previous expression for Δx, we obtain
    Mpulse = Mbox Δ x / L = Mbox  / L × El / MBox c² =   E /c²
Or E = Mpulse c².
    The energy of a system of particles before interaction must equal the energy of the system after interaction, where energy of the ith particle is given by the expression Ei = γ mi c².
Thus, Einstein reached the profound conclusion that “if a body gives off the energy E in the form of radiation, its mass diminishes by     E /c², ..."
    Although we derived the relationship E = m c² for light energy, the equivalence of mass and energy is universal.
Equation E = γ m c², which represents the total energy of any particle, suggests that even when a particle is at rest - γ = 1 - it still possesses enormous energy because it has mass. Probably the clearest experimental proof of the equivalence of mass and energy occurs in nuclear and elementary particle interactions, where large amounts of energy are released and the energy release is accompanied by a decrease in mass. Because energy and mass are related, we see that the laws of conservation of energy and conservation of mass are one and the same. Simply put, this law states that
    The release of enormous quantities of energy from subatomic particles, accompanied by changes in their masses, is the basis of all nuclear reactions. In a conventional nuclear reactor, a uranium nucleus undergoes fission, a reaction that creates several lighter fragments having considerable kinetic energy. The combined mass of all the fragments is less than the mass of the parent uranium nucleus by an amount Δ m. The corresponding energy Δ mc² associated with this mass difference is exactly equal to the total kinetic energy of the fragments. This kinetic energy raises the temperature of water in the reactor, converting it to steam for the generation of electric power.
    In the nuclear reaction called fusion, two atomic nuclei combine to form a single nucleus. The fusion reaction in which two deuterium nuclei fuse to form a helium nucleus is of major importance in current research and the development of controlled-fusion reactors. The decrease in mass that results from the creation of one helium nucleus from two deuterium nuclei is Δ m = 4.25 × 10 -29 kg. Hence, the corresponding excess energy that results from one fusion reaction is  Δ mc² = 3.38 × 10-12 J - Joul-= 23.9 Mev.To appreciate the magnitude of this result, note that if 1 g of deuterium is converted to helium, the energy released is about 1012 J !At the current cost of electrical energy, this quantity of energy would be worth about               $70 000 .That is a lot of money!.
    Coming up : RELATIVITY AND ELECTROMAGNETISM.