What Is Reduced Mass?

The so-called mass loss is the change in the mass of the system particles before and after the reaction. For example, in nuclear reactions, it means the difference between the mass of the nucleus and the sum of the masses of all the individual protons and neutrons that make up the nucleus (the mass of the nucleus is less than the sum of the masses of all the individual protons and single neutrons that make up the nucleus. The binding energy, the greater the loss, the greater the binding energy).

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According to Einstein's mass energy equation E = mc ² , a certain mass m corresponds to a certain energy E , and the quantitative relationship between the two is related by the proportionality coefficient square of the speed of light c ² . Due to the energy conversion during the nuclear reaction, the static energy E = mc ² contained in the particles before and after the nuclear reaction may change, so the static mass will increase or decrease before and after the reaction. If the nuclear reaction absorbs energy, the static mass before and after the nuclear reaction will increase; if the nuclear reaction releases energy, the static mass will decrease. The reduced mass is the loss mass m in the nuclear reaction, then the nuclear energy released by the nuclear reaction E = mc ² . Both heavy nuclear fission and light nuclear fusion belong to exothermal nuclear reactions. The static mass of particles before and after the reaction must be reduced, that is, the mass must be lost, and the mass loss means a loss of energy, and the lost energy is the atomic energy of the nucleus.

From the perspective of the law of conservation of energy, the static energy mc ² corresponding to this deficient mass m is converted into the kinetic energy of particles or the energy of photons (ie, energy rays).

Mass loss in chemical reactions

Chemical reactions are much milder than those discussed earlier, but they also follow the mass-energy equation. When a chemical reaction occurs and energy is released, the equivalent mass must be lost. But because most chemical reactions release much less energy than common nuclear reactions. Therefore, compared to nuclear reactions, the mass loss of chemical reactions is often so small that even the most sophisticated instruments cannot measure them, and can only be estimated by the energy released by the reaction. This is why, after Lavoisier discovered the law of conservation of mass, no chemist found any counterexample in the laboratory.

Strictly speaking, the quality of the system in chemical reactions is also non-conservative. With this in mind, we should say that there are no detectable quality changes before and after the reaction. Just as two gold coins were left from the truck, since the mass of the two gold coins is too small relative to the weight of the truck, it seems that the quality of the truck has not changed.

Taking the explosion of nitroglycerin as an example, assuming that the initial state of the reaction is the standard condition of 25 ° C, the mass loss before and after the reaction can be calculated:
4C ₃ H ₅ N ₃ O ₉ (l) 6N ₂ (g) + 12CO (g) + 10H ₂ O (l) + 7O ₂ (g), H = 2700kJ
The energy released by the reaction system is equal to the sum of heat and work: E = H p V = H nRT
Where n is the change amount of the gas before and after the reaction. p V = 62kJ
So E = 2762kJ, the corresponding mass equivalent should be E / c ² = 3.074 × 10 ^-8 g.

The mass of any nucleus is less than the sum of the rest masses of the protons and neutrons that make them up. The mass loss of such nuclei is caused by the process of nucleus formation. The rest masses of protons and neutrons are 1.007276u and 1.098665u, respectively. The quality is 2.013553u. Therefore, the mass loss is 0.002388u, and its energy equivalent is 3.564 × 10 ^-13 J, which is the energy released by the reaction, that is, the binding energy of the nucleus.

The same is true for chemical changes, such as the reaction of C + 4H CH _4. The energy released by the reaction is 2.916 × 10 ^-18 J / molecule, and the mass loss in the reaction is 1.954 × 10 ^-8 u, which is far less than the formation of ² H nuclei. Quality loss at the time. Mass loss during the formation of ² H was 0.12%, while mass loss during the formation of methane molecules was 0.000031%.

¹² C is used as a standard to define the atomic weight, and its resting mass is 12u. We can calculate the mass of the atom under different conditions, such as when the atom is heated to obtain kinetic energy, or when the atom is bonded to form graphite or diamond, and the chemical energy is consumed, the atom's mass will change, see the table below. The conversion between graphite and diamond can be considered as a mass loss. Although the magnitude of this mass loss is very weak, it is enough to attract the attention of chemists. Chemists should always remind themselves that the quality of the atom is close to the chemical state of the atom related.

The table is the atomic mass of ¹² C in different chemical states. ^[2]

status	Atomic mass / u
Static mass of an isolated atom	12.000000000000
Isolated atom (298K)	12.000000000045
Graphite (298K)	11.999999992116
Diamond (298K)	11.999999992137