To understand how to balance nuclear reactions and calculate reaction energies.
ID: 2076633 • Letter: T
Question
To understand how to balance nuclear reactions and calculate reaction energies. A nuclear reaction is represented by an equation similar to the equation for a chemical reaction. An example of a nuclear reaction is the decay of radium into radon by the emission of an alpha particle (a helium nucleus). The equation for this reaction is 226 88Ra222 86Rn+42He. The superscript preceding each element indicates the nucleon number of that particular nucleus (total number of protons and neutrons). The subscript indicates the charge of the nucleus, which is equal to the atomic number for nuclei. Nuclear reactions frequently involve electrons (sometimes called beta rays) and photons (sometimes called gamma rays). Electrons, which have nucleon number 0 and charge 1, are represented in equations as either 01 or 01e. Photons are represented as 00 to emphasize that they have no nucleon number and carry no charge. In nuclear reactions, several conservation laws are usually sufficient to determine the products or reactants. One of these is conservation of nucleon number. The total number of neutrons and protons in all of the reactants must be the same as the total number of protons and neutrons in the products. Although protons and neutrons sometimes change into one another, neither can simply disappear. Another important conservation law is conservation of charge. The net charge of the reactants must be the same as that of the products. Notice that, in our equation for the decay of radium, the sum of the nucleon numbers on each side is 226 and the sum of the charges on each side is 88. If you knew everything in this equation except the isotope of radon produced, you could simply subtract 4 from 226 to find the nucleon number required to make the nucleon number of the products equal the nucleon number of the reactants. Similarly, if you knew everything in this equation except for the identity of the product element, you could simply subtract 2 from 88 and then look in a periodic table to find that the element with atomic number 86 is radon.
C. Consider the decay of Potassium-43 into calcium-43 via the following reaction: 43/19K43/20Ca+X.
What is the charge of the emitted particle X?
E.An isotope of potassium with a half-life of roughly one billion years is often used in radioactive dating. This isotope decays through electron capture, the process of drawing an electron into the nucleus. What is the chemical symbol for the element that results from this process?
F.The equation for the reaction is 40/19K+ 01e? The reaction energy of a reaction is the amount of energy released by the reaction. It is found by determining the difference in mass between the reactants and products and then using E=mc2 to convert the lost mass into the released energy. Look again at the equation for the decay of radium (Ra), given in the introduction. Use the following table of masses to determine the reaction energy of this reaction. Nucleus or particle Mass in atomic mass units radium-226 =226.025402 radon-222=222.017571 alpha particle=4.002602 =J
Explanation / Answer
C. For a given reaction, 43 19K -> 43 20Ca + A ZX
where A is the mass no. for species X and Z is the proton no.
As per mass no. and charge conservation,
43 = 43 + A
A = 0
also, 19 = 20 + Z, Z = -1 -ve charge, zero proton
the species X is an electron with charge -e
E. 43 19K + 0 -1e -> 43 18Ar, species is Argon.
F. 226 88Ra222 86Rn+4 2He,
Mass difference = Mass of Reactants - Mass of products = 226.025402 - [222.017571 + 4.002602]
= 226.025402 - 226.020173 = 0.005229 amu
1 amu = 931.25 MeV / c2
Reaction energy, E = (Mass difference) c2 = 0.005229*931.25 MeV = 4.8695 MeV
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