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What do the three types of beta decay have in common that is distinctly different from alpha decay?

Problems&Exercises

In the following eight problems, write the complete decay equation for the given nuclide in the complete Z A X N size 12{"" lSub { size 8{Z} } lSup { size 8{A} } X rSub { size 8{N} } } {} notation. Refer to the periodic table for values of Z size 12{Z} {} .

β size 12{β rSup { size 8{ - {}} } } {} decay of 3 H size 12{"" lSup { size 8{3} } H} {} (tritium), a manufactured isotope of hydrogen used in some digital watch displays, and manufactured primarily for use in hydrogen bombs.

1 3 H 2 2 3 He 1 + β + ν ¯ e

β size 12{β rSup { size 8{ - {}} } } {} decay of 40 K size 12{"" lSup { size 8{"40"} } K} {} , a naturally occurring rare isotope of potassium responsible for some of our exposure to background radiation.

β + size 12{β rSup { size 8{+{}} } } {} decay of 50 Mn size 12{"" lSup { size 8{"50"} } "Mn"} {} .

25 50 M 25 24 50 Cr 26 + β + + ν e size 12{"" lSub { size 8{"25"} } lSup { size 8{"50"} } M rSub { size 8{"25"} } rightarrow "" lSub { size 8{"24"} } lSup { size 8{"50"} } "Cr" rSub { size 8{"20"} } +β rSup { size 8{+{}} } +v rSub { size 8{e} } } {}

β + size 12{β rSup { size 8{+{}} } } {} decay of 52 Fe size 12{"" lSup { size 8{"52"} } "Fe"} {} .

Electron capture by 7 Be size 12{"" lSup { size 8{7} } "Be"} {} .

4 7 Be 3 + e 3 7 Li 4 + ν e size 12{"" lSub { size 8{4} } lSup { size 8{7} } "Be" rSub { size 8{3} } +e rSup { size 8{ - {}} } rightarrow "" lSub { size 8{3} } lSup { size 8{7} } "Li" rSub { size 8{4} } +v rSub { size 8{e} } } {}

Electron capture by 106 In size 12{"" lSup { size 8{"106"} } "In"} {} .

α size 12{α} {} decay of 210 Po size 12{"" lSup { size 8{"210"} } "Po"} {} , the isotope of polonium in the decay series of 238 U size 12{"" lSup { size 8{"238"} } U} {} that was discovered by the Curies. A favorite isotope in physics labs, since it has a short half-life and decays to a stable nuclide.

84 210 Po 126 82 206 Pb 124 + 2 4 He 2 size 12{"" lSub { size 8{"84"} } lSup { size 8{"210"} } "Pb" rSub { size 8{"126"} } rightarrow "" lSub { size 8{"82"} } lSup { size 8{"206"} } "Pb" rSub { size 8{"124"} } +"" lSub { size 8{2} } lSup { size 8{4} } "He" rSub { size 8{2} } } {}

α size 12{α} {} decay of 226 Ra size 12{"" lSup { size 8{"226"} } "Ra"} {} , another isotope in the decay series of 238 U size 12{"" lSup { size 8{"238"} } U} {} , first recognized as a new element by the Curies. Poses special problems because its daughter is a radioactive noble gas.

In the following four problems, identify the parent nuclide and write the complete decay equation in the Z A X N size 12{"" lSub { size 8{Z} } lSup { size 8{A} } X rSub { size 8{N} } } {} notation. Refer to the periodic table for values of Z size 12{Z} {} .

β size 12{β rSup { size 8{ - {}} } } {} decay producing 137 Ba size 12{"" lSup { size 8{"137"} } "Ba"} {} . The parent nuclide is a major waste product of reactors and has chemistry similar to potassium and sodium, resulting in its concentration in your cells if ingested.

55 137 Cs 82 56 137 Ba 81 + β + ν ¯ e size 12{"" lSub { size 8{"55"} } lSup { size 8{"137"} } "Cs" rSub { size 8{"82"} } rightarrow "" lSub { size 8{"56"} } lSup { size 8{"137"} } "Ba" rSub { size 8{"81"} } +β rSup { size 8{ - {}} } + {overline {v rSub { size 8{e} } }} } {}

β size 12{β rSup { size 8{ - {}} } } {} decay producing 90 Y size 12{"" lSup { size 8{"90"} } Y} {} . The parent nuclide is a major waste product of reactors and has chemistry similar to calcium, so that it is concentrated in bones if ingested ( 90 Y size 12{"" lSup { size 8{"90"} } Y} {} is also radioactive.)

α size 12{α} {} decay producing 228 Ra size 12{"" lSup { size 8{"228"} } "Ra"} {} . The parent nuclide is nearly 100% of the natural element and is found in gas lantern mantles and in metal alloys used in jets ( 228 Ra size 12{"" lSup { size 8{"228"} } "Ra"} {} is also radioactive).

90 232 Th 142 88 228 Ra 140 + 2 4 He 2 size 12{"" lSub { size 8{"90"} } lSup { size 8{"232"} } "Th" rSub { size 8{"142"} } rightarrow "" lSub { size 8{"88"} } lSup { size 8{"228"} } "Ra" rSub { size 8{"140"} } +"" lSub { size 8{2} } lSup { size 8{4} } "He" rSub { size 8{2} } } {}

α size 12{α} {} decay producing 208 Pb size 12{"" lSup { size 8{"208"} } "Pb"} {} . The parent nuclide is in the decay series produced by 232 Th size 12{"" lSup { size 8{"232"} } "Th"} {} , the only naturally occurring isotope of thorium.

When an electron and positron annihilate, both their masses are destroyed, creating two equal energy photons to preserve momentum. (a) Confirm that the annihilation equation e + + e γ + γ size 12{e rSup { size 8{+{}} } +e rSup { size 8{ - {}} } rightarrow γ+γ} {} conserves charge, electron family number, and total number of nucleons. To do this, identify the values of each before and after the annihilation. (b) Find the energy of each γ size 12{γ} {} ray, assuming the electron and positron are initially nearly at rest. (c) Explain why the two γ size 12{γ} {} rays travel in exactly opposite directions if the center of mass of the electron-positron system is initially at rest.

(a) charge: + 1 + 1 = 0 ; electron family number: + 1 + 1 = 0 ; A : 0 + 0 = 0

(b) 0.511 MeV

(c) The two γ size 12{γ} {} rays must travel in exactly opposite directions in order to conserve momentum, since initially there is zero momentum if the center of mass is initially at rest.

Confirm that charge, electron family number, and the total number of nucleons are all conserved by the rule for α decay given in the equation Z A X N Z 2 A 4 Y N 2 + 2 4 He 2 . To do this, identify the values of each before and after the decay.

Confirm that charge, electron family number, and the total number of nucleons are all conserved by the rule for β decay given in the equation Z A X N Z + 1 A Y N 1 + β + ν ¯ e size 12{"" lSub { size 8{Z} } lSup { size 8{A} } X rSub { size 8{N} } rightarrow "" lSub { size 8{Z−1} } lSup { size 8{A} } Y rSub { size 8{N - 1} } +β rSup { size 8{ - {}} } + {overline {v rSub { size 8{e} } }} } {} . To do this, identify the values of each before and after the decay.

Z = Z + 1 1; A = A ; efn : 0 = + 1 + 1

Confirm that charge, electron family number, and the total number of nucleons are all conserved by the rule for β size 12{β rSup { size 8{ - {}} } } {} decay given in the equation Z A X N Z 1 A Y N 1 + β + ν e . To do this, identify the values of each before and after the decay.

Confirm that charge, electron family number, and the total number of nucleons are all conserved by the rule for electron capture given in the equation Z A X N + e Z 1 A Y N + 1 + ν e size 12{"" lSub { size 8{Z} } lSup { size 8{A} } X rSub { size 8{N} } +e rSup { size 8{ - {}} } rightarrow "" lSub { size 8{Z - 1} } lSup { size 8{A} } Y rSub { size 8{N+1} } +v rSub { size 8{e} } } {} . To do this, identify the values of each before and after the capture.

Z - 1 = Z 1; A = A ; efn : + 1 = + 1 alignl { stack { size 12{Z+1=Z - 1" before/after; captured "e rSup { size 8{ - 1} } " is last term rhs;"} {} #A=A" ; efn : " left (+1 right )= left (+1 right ) {} } } {}

A rare decay mode has been observed in which 222 Ra emits a 14 C nucleus. (a) The decay equation is 222 Ra A X+ 14 C size 12{ {} rSup { size 8{"222"} } "Ra" rightarrow rSup { size 8{A} } "X+" rSup { size 8{"14"} } C} {} . Identify the nuclide A X . (b) Find the energy emitted in the decay. The mass of 222 Ra size 12{"" lSup { size 8{"222"} } "Ra"} {} is 222.015353 u.

(a) Write the complete α size 12{α} {} decay equation for 226 Ra size 12{"" lSup { size 8{"226"} } "Ra"} {} .

(b) Find the energy released in the decay.

(a) 88 226 Ra 138 86 222 Rn 136 + 2 4 He 2

(b) 4.87 MeV

(a) Write the complete α size 12{α} {} decay equation for 249 Cf size 12{"" lSup { size 8{"249"} } "Cf"} {} .

(b) Find the energy released in the decay.

(a) Write the complete β size 12{β rSup { size 8{ - {}} } } {} decay equation for the neutron. (b) Find the energy released in the decay.

(a) n p + β + ν ¯ e

(b) ) 0.783 MeV

(a) Write the complete β size 12{β rSup { size 8{ - {}} } } {} decay equation for 90 Sr size 12{"" lSup { size 8{"90"} } "Sr"} {} , a major waste product of nuclear reactors. (b) Find the energy released in the decay.

Calculate the energy released in the β + size 12{β rSup { size 8{+{}} } } {} decay of 22 Na , the equation for which is given in the text. The masses of 22 Na and 22 Ne size 12{"" lSup { size 8{"22"} } "Ne"} {} are 21.994434 and 21.991383 u, respectively.

1.82 MeV

(a) Write the complete β + size 12{β rSup { size 8{+{}} } } {} decay equation for 11 C size 12{"" lSup { size 8{"11"} } C} {} .

(b) Calculate the energy released in the decay. The masses of 11 C size 12{"" lSup { size 8{"11"} } C} {} and 11 B size 12{"" lSup { size 8{"11"} } B} {} are 11.011433 and 11.009305 u, respectively.

(a) Calculate the energy released in the α size 12{α} {} decay of 238 U size 12{"" lSup { size 8{"238"} } U} {} .

(b) What fraction of the mass of a single 238 U size 12{"" lSup { size 8{"238"} } U} {} is destroyed in the decay? The mass of 234 Th size 12{"" lSup { size 8{"234"} } "Th"} {} is 234.043593 u.

(c) Although the fractional mass loss is large for a single nucleus, it is difficult to observe for an entire macroscopic sample of uranium. Why is this?

(a) 4.274 MeV

(b) 1 . 927 × 10 5 size 12{1 "." "927" times "10" rSup { size 8{ - 5} } u} {}

(c) Since U-238 is a slowly decaying substance, only a very small number of nuclei decay on human timescales; therefore, although those nuclei that decay lose a noticeable fraction of their mass, the change in the total mass of the sample is not detectable for a macroscopic sample.

(a) Write the complete reaction equation for electron capture by 7 Be. size 12{"" lSup { size 8{7} } "Be"} {}

(b) Calculate the energy released.

(a) Write the complete reaction equation for electron capture by 15 O size 12{"" lSup { size 8{"15"} } O} {} .

(b) Calculate the energy released.

(a) 8 15 O 7 + e 7 15 N 8 + ν e size 12{"" lSub { size 8{8} } lSup { size 8{"15"} } O rSub { size 8{7} } +e rSup { size 8{ - {}} } rightarrow "" lSub { size 8{7} } lSup { size 8{"15"} } N rSub { size 8{8} } +v rSub { size 8{e} } } {}

(b) 2.754 MeV

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Source:  OpenStax, Concepts of physics. OpenStax CNX. Aug 25, 2015 Download for free at https://legacy.cnx.org/content/col11738/1.5
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