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

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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
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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.

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

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

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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} } } {}
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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.

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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} } }} } {}
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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.)

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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} } } {}
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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.

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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.

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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.

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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
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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.

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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 ) {} } } {}
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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.

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(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

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(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.

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(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

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(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.

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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

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(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.

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(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.

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

(b) Calculate the energy released.

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(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, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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