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Note that the daughters of α size 12{α} {} decay shown in [link] always have two fewer protons and two fewer neutrons than the parent. This seems reasonable, since we know that α size 12{α} {} decay is the emission of a 4 He size 12{"" lSup { size 8{4} } "He"} {} nucleus, which has two protons and two neutrons. The daughters of β size 12{β} {} decay have one less neutron and one more proton than their parent. Beta decay is a little more subtle, as we shall see. No γ size 12{γ} {} decays are shown in the figure, because they do not produce a daughter that differs from the parent.

Alpha decay

In alpha decay    , a 4 He size 12{"" lSup { size 8{4} } "He"} {} nucleus simply breaks away from the parent nucleus, leaving a daughter with two fewer protons and two fewer neutrons than the parent (see [link] ). One example of α size 12{α} {} decay is shown in [link] for 238 U size 12{"" lSup { size 8{"238"} } U} {} . Another nuclide that undergoes α size 12{α} {} decay is 239 Pu size 12{"" lSup { size 8{"239"} } "Pu"} {} . The decay equations for these two nuclides are

238 U 234 Th 92 234 + 4 He

and

239 Pu 235 U + 4 He . size 12{"" lSup { size 8{"239"} } "Pu" rightarrow "" lSup { size 8{"235"} } U+"" lSup { size 8{4} } "He"} {}
The image shows conditions before and after alpha decay. Before alpha decay the nucleus is labeled parent and after decay the nucleus is labeled daughter.
Alpha decay is the separation of a 4 He size 12{"" lSup { size 8{4} } "He"} {} nucleus from the parent. The daughter nucleus has two fewer protons and two fewer neutrons than the parent. Alpha decay occurs spontaneously only if the daughter and 4 He size 12{"" lSup { size 8{4} } "He"} {} nucleus have less total mass than the parent.

If you examine the periodic table of the elements, you will find that Th has Z = 90 size 12{Z="90"} {} , two fewer than U, which has Z = 92 size 12{Z="92"} {} . Similarly, in the second decay equation    , we see that U has two fewer protons than Pu, which has Z = 94 size 12{Z="94"} {} . The general rule for α size 12{α} {} decay is best written in the format Z A X N . If a certain nuclide is known to α size 12{α} {} decay (generally this information must be looked up in a table of isotopes, such as in [link] ), its α size 12{α} {} decay equation    is

Z A X N Z 2 A 4 Y N 2 + 2 4 He 2 ( α decay ) size 12{α} {}

where Y is the nuclide that has two fewer protons than X, such as Th having two fewer than U. So if you were told that 239 Pu α decays and were asked to write the complete decay equation, you would first look up which element has two fewer protons (an atomic number two lower) and find that this is uranium. Then since four nucleons have broken away from the original 239, its atomic mass would be 235.

It is instructive to examine conservation laws related to α size 12{α} {} decay. You can see from the equation Z A X N Z 2 A 4 Y N 2 + 2 4 He 2 that total charge is conserved. Linear and angular momentum are conserved, too. Although conserved angular momentum is not of great consequence in this type of decay, conservation of linear momentum has interesting consequences. If the nucleus is at rest when it decays, its momentum is zero. In that case, the fragments must fly in opposite directions with equal-magnitude momenta so that total momentum remains zero. This results in the α size 12{α} {} particle carrying away most of the energy, as a bullet from a heavy rifle carries away most of the energy of the powder burned to shoot it. Total mass–energy is also conserved: the energy produced in the decay comes from conversion of a fraction of the original mass. As discussed in [link] , the general relationship is

E = ( Δ m ) c 2 .

Here, E size 12{E} {} is the nuclear reaction energy    (the reaction can be nuclear decay or any other reaction), and Δ m size 12{Δm} {} is the difference in mass between initial and final products. When the final products have less total mass, Δ m size 12{Δm} {} is positive, and the reaction releases energy (is exothermic). When the products have greater total mass, the reaction is endothermic ( Δ m size 12{Δm} {} is negative) and must be induced with an energy input. For α size 12{α} {} decay to be spontaneous, the decay products must have smaller mass than the parent.

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Source:  OpenStax, College physics for ap® courses. OpenStax CNX. Nov 04, 2016 Download for free at https://legacy.cnx.org/content/col11844/1.14
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