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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

Questions & Answers

find the 15th term of the geometric sequince whose first is 18 and last term of 387
Jerwin Reply
I know this work
salma
The given of f(x=x-2. then what is the value of this f(3) 5f(x+1)
virgelyn Reply
hmm well what is the answer
Abhi
how do they get the third part x = (32)5/4
kinnecy Reply
can someone help me with some logarithmic and exponential equations.
Jeffrey Reply
sure. what is your question?
ninjadapaul
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
ninjadapaul
I don't understand what the A with approx sign and the boxed x mean
ninjadapaul
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
ninjadapaul
oops. ignore that.
ninjadapaul
so you not have an equal sign anywhere in the original equation?
ninjadapaul
hmm
Abhi
is it a question of log
Abhi
🤔.
Abhi
I rally confuse this number And equations too I need exactly help
salma
But this is not salma it's Faiza live in lousvile Ky I garbage this so I am going collage with JCTC that the of the collage thank you my friends
salma
Commplementary angles
Idrissa Reply
hello
Sherica
im all ears I need to learn
Sherica
right! what he said ⤴⤴⤴
Tamia
hii
Uday
hi
salma
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
Kevin Reply
a perfect square v²+2v+_
Dearan Reply
kkk nice
Abdirahman Reply
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
Kim Reply
or infinite solutions?
Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
y=10×
Embra Reply
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
Nancy Reply
rolling four fair dice and getting an even number an all four dice
ramon Reply
Kristine 2*2*2=8
Bridget Reply
Differences Between Laspeyres and Paasche Indices
Emedobi Reply
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
Mary Reply
how do you translate this in Algebraic Expressions
linda Reply
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
AMJAD
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
AMJAD
what is system testing
AMJAD
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
can nanotechnology change the direction of the face of the world
Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
Ali Reply
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
bamidele Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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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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