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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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Questions & Answers

a thick glass cup cracks when hot liquid is poured into it suddenly
Aiyelabegan Reply
because of the sudden contraction that takes place.
Eklu
railway crack has gap between the end of each length because?
Aiyelabegan Reply
For expansion
Eklu
yes
Aiyelabegan
Please i really find it dificult solving equations on physic, can anyone help me out?
Big Reply
sure
Carlee
what is the equation?
Carlee
Sure
Precious
fersnels biprism spectrometer how to determined
Bala Reply
how to study the hall effect to calculate the hall effect coefficient of the given semiconductor have to calculate the carrier density by carrier mobility.
Bala
what is the difference between atomic physics and momentum
Nana Reply
find the dimensional equation of work,power,and moment of a force show work?
Emmanuel Reply
What's sup guys
Peter
cul and you all
Okeh
cool you bro
Nana
so what is going on here
Nana
hello peeps
Joseph
Michelson Morley experiment
Riya Reply
how are you
Naveed
am good
Celine
you
Celine
hi
Bala
Hi
Ahmed
Calculate the final velocity attained, when a ball is given a velocity of 2.5m/s, acceleration of 0.67m/s² and reaches its point in 10s. Good luck!!!
Eklu Reply
2.68m/s
Doc
vf=vi+at vf=2.5+ 0.67*10 vf= 2.5 + 6.7 vf = 9.2
babar
s = vi t +1/2at sq s=58.5 s=v av X t vf= 9.2
babar
how 2.68
babar
v=u+at where v=final velocity u=initial velocity a=acceleration t=time
Eklu
the answer is 9.2m/s
OBERT
express your height in Cm
Emmanuel Reply
my project is Sol gel process how to prepare this process pls tell me
Bala
the dimension of work and energy is ML2T2 find the unit of work and energy hence drive for work?
Emmanuel Reply
KgM2S2
Acquah
Two bodies P and Quarter each of mass 1000g. Moved in the same direction with speed of 10m/s and 20m/s respectively. Calculate the impulse of P and Q obeying newton's 3rd law of motion
Shimolla Reply
kk
Doc
the answer is 0.03n according to the 3rd law of motion if the are in same direction meaning they interact each other.
OBERT
definition for wave?
Doc Reply
A disturbance that travel from one medium to another and without causing permanent change to its displacement
Fagbenro
In physics, a wave is a disturbance that transfers energy through matter or space, with little or no associated mass transport (Mass transfer). ... There are two main types ofwaves: mechanical and electromagnetic. Mechanicalwaves propagate through a physical matter, whose substance is being deformed
Devansh
K
Manyo
thanks jare
Doc
Thanks
AMADI
Note: LINEAR MOMENTUM Linear momentum is defined as the product of a system’s mass multiplied by its velocity: size 12{p=mv} {}
AMADI
what is physic
zalmia Reply
please gave me answar
zalmia
Study of matter and energy
Fagbenro
physics is the science of matter and energy and their interactions
Acquah
physics is the technology behind air and matter
Doc
Okay
William
hi sir
Bala
how easy to understanding physics sir
Bala
Easy to learn
William
31. Calculate the initial (from rest) acceleration of a proton in a 5.00×106 N/C electric field (such as created by a research Van de Graaff). Explicitly show how you follow the steps in the Problem-Solving Strategy for electrostatics.
Catina Reply
A tennis ball is projected at an angle and attains a range of 78. if the velocity is 30metres per second, calculate the angle
Shimolla
what friction
Wisdom Reply
question on friction
Wisdom
the rubbing of one object or surface against another.
author
momentum is the product of mass and it's velocity.
Algayawi
what are bioelements?
Edina
Friction is a force that exist between two objects in contact. e.g. friction between road and car tires.
Eklu

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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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