Alpha Decay Half-Lives of Notable Light Isotopes: Estimates and Unknowns

In summary: Hg you get one, and it´s the only one before Pb.81 - Tl - 911 keV Tl-20382 - Pb - 391 keV Pb-207. Stable isotope.83 - Bi - 3137 keV Bi-209, able to single beta and double beta decay. Of double beta stable isotopes, 519 keV Bi-20884 - Po - no alpha decay85 - At - no alpha decay86 - Rn - alpha... alpha... alpha... not until 222Rn you get one. All others alpha decay.87 - Fr - alpha... alpha... alpha... not until 228Fr you get one
  • #1
snorkack
2,190
477
What is supposed to be the lifetime of lead against alpha decay?

Notable light isotopes that DO undergo alpha decay:
Be-8 188 keV 7*10ˇ-16 s
Sm-146 2529 keV 103*10ˇ6 y
U-235 4679 keV 704*10ˇ6 y
U-238 4270 keV 4,47*10ˇ9 y
Th-232 4083 keV 14,06*10ˇ9 y
Sm-147 2310 keV 106,1*10ˇ9 y
Pt-190 3252 keV 650*10ˇ9 y
Gd-152 2203 keV 110*10ˇ12 y
Hf-174 2497 keV 2*10ˇ15 y
Os-186 2823 keV 2*10ˇ15 y
Nd-144 1905 keV 2,3*10ˇ15 y
Sm-148 1986 keV 7*10ˇ15 y
W-180 2509 keV 1,8*10ˇ18 y
Eu-151 1964 keV 5*10ˇ18 y
Bi-209 3137 keV 19*10ˇ18 y

Now isotopes which might release rest mass energy by alpha decay, but do NOT:
Os-184 2963 keV
Os-187 2720 keV
Pt-192 2418 keV
Hf-176 2255 keV
Hf-177 2245 keV
Re-185 2195 keV
Os-188 2143 keV
Ta-180 2103 keV
Ir-191 2084 keV
Hf-178 2083 keV
Hg-196 2027 keV
Os-189 1976 keV
Pb-204 1972 keV
Yb-168 1951 keV
Sm-149 1870 keV
Hf-179 1806 keV
W-182 1772 keV
Dy-156 1758 keV
Yb-170 1738 keV
W-183 1680 keV
W-186 1656 keV
Er-162 1646 keV
Lu-175 1620 keV
Nd-145 1578 keV
Yb-171 1559 keV
Ta-181 1526 keV
Pt-194 1504 keV
Sm-150 1449 keV
Hg-198 1383 keV
Os-190 1378 keV
Yb-172 1310 keV
Er-164 1304 keV
Ce-142 1298 keV
Hf-180 1283 keV
Tm-169 1200 keV
Nd-146 1182 keV
Pt-195 1158 keV
Pb-206 1137 keV
W-186 1123 keV
Ir-193 1017 keV
Au-197 954 keV
Yb-173 946 keV
Tl-203 911 keV
Dy-158 875 keV
Er-166 831 keV
Hg-199 824 keV
Pt-196 794 keV
Yb-174 740 keV
Hg-200 718 keV
Er-167 666 keV
Nd-148 599 keV
Yb-176 570 keV
Er-168 553 keV
Nd-143 521 keV
Pb-208 519 keV
Dy-160 439 keV
Pb-207 391 keV
Os-192 362 keV
Dy-161 344 keV
Hg-201 334 keV
Eu-153 274 keV
Sm-152 220 keV
Tl-205 157 keV
Ho-165 139 keV
Hg-202 136 keV
Pt-198 87 keV
Dy-162 85 keV
Gd-155 81 keV
Gd-154 81 keV
Sm-144 76 keV
Er-170 50 keV

So, what are the estimates for the half-lives of the above isotopes not known to decay?
 
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  • #2
http://atom.kaeri.re.kr/ton/
Above contains the information you are looking for.

I looked at the Os isotopes. 184 has extremely long half life. Os-187 is stable.
 
  • #3
So, what are the estimates for the half-lives of the above isotopes not known to decay?
If the isotope is not known to decay, then it's half-life is estimated as "infinite". That is what "stable" means
Pb208, for instance, is the heaviest known stable nucleus.

You can look up decay rates in tables of isotopes - which you can find in a college library or a teaching lab than includes radioactivity experiments. There are quite a few online too:
i.e. http://ie.lbl.gov/toi/nuclide.asp?iZA=820210 (Pb210)
http://atom.kaeri.re.kr/ton/

Wikipedia has the usual graphic showing the distribution of different decay modes.
 
  • #4
U-235 4679 keV 704*10ˇ6 y
U-238 4270 keV 4,47*10ˇ9 y
Th-232 4083 keV 14,06*10ˇ9 y
Bi-209 3137 keV 19*10ˇ18 y

are not considered light isotopes. They are considered heavy, and certainly heaviest of the naturally occurring isotopes, except for Bi- which is not as heavy as the U-isotopes.
 
  • #5
mathman said:
http://atom.kaeri.re.kr/ton/
Above contains the information you are looking for.

I looked at the Os isotopes. 184 has extremely long half life. Os-187 is stable.
Look further.
That 56*10ˇ12 years is lower bound! No upper bound, therefore no decay.

How come that a natural isotope with no upper bound of half-life has a lower bound as short as 56*10ˇ12 years, seeing that bismuth has upper bound of alpha decay lifetime at 19*10ˇ18 years, and even longer upper bounds are observed for some double beta decays?

Also, for the isotopes that do have observed long lifetimes, how well do the observed values fit theoretical predictions?
Now, most of these known long-lived isotopes:
Pt-190 3252 keV 650*10ˇ9 y
Gd-152 2203 keV 110*10ˇ12 y
Hf-174 2497 keV 2*10ˇ15 y
Os-186 2823 keV 2*10ˇ15 y
Nd-144 1905 keV 2,3*10ˇ15 y
Sm-148 1986 keV 7*10ˇ15 y
W-180 2509 keV 1,8*10ˇ18 y
are even-even. Easy. Mother even-even, ground state spin zero, alpha even-even ground state spin zero, daughter even-even ground state spin zero. No complications.
But how about
Eu-151 1964 keV 5*10ˇ18 y 5/2+ daughter Pm-147 7/2+ and beta lifetime 2,6 y
Bi-209 3137 keV 19*10ˇ18 y 9/2- daughter Tl-205 1/2+
Do their lifetimes match forecasts?
 
  • #6
snorkack said:
How come that a natural isotope with no upper bound of half-life has a lower bound as short as 56*10ˇ12 years, seeing that bismuth has upper bound of alpha decay lifetime at 19*10ˇ18 years, and even longer upper bounds are observed for some double beta decays?
Different experimental challenges (like: how clean do you get your sample, especially if other natural isotopes of the element are radioactive) and different interest in the various isotopes.
Beta decay is way easier to measure as you get an electron out. Or even two in coincidence in case of double beta decay.
 
  • #7
snorkack said:
So, what are the estimates for the half-lives of the above isotopes not known to decay?

You should clarify if you are asking for lower bounds or for theoretical estimates. I'd like to hear about the second.
 
  • #8
arivero said:
You should clarify if you are asking for lower bounds or for theoretical estimates. I'd like to hear about the second.
So would I. I wouldn´t expect experimental lower bounds to be significant for lead.
Tried looking at it another way: the minimum alpha decay energy of isotopes by element.
59 - Pr - no alpha decay
60 - Nd - 4 isotopes can release energy by alpha decay, but not 142-Nd
61 - Pm - all isotopes unstable to single beta
62 - Sm - 76 keV of Sm-144, which also is able to double electron capture. Of double beta stable isotopes, 220 keV Sm-152
63 - Eu - 274 keV Eu-153
64 - Gd - 3 isotopes stable to alpha
65 - Tb - stable to alpha
66 - Dy - 2 isotopes stable to alpha. Dy-164 is the heaviest nucleus which qualifies to that and also is stable to double beta.
67 - Ho - 139 keV Ho-165
68 - Er - 50 keV of Er-170, which also is able to double beta decay. Of double beta stable isotopes, 553 keV Er-168
69 - Tm - 1200 keV Tm-169
70 - Yb - 570 kev Yb-176, also able to double beta decay. Of double beta stable isotopes, 740 keV Yb-174
71 - Lu - 1620 keV Lu-175
72 - Hf - 1283 keV Hf-180
73 - Ta - 1526 keV Ta-181
74 - W - 1123 keV W-186
75 - Re - 2195 keV Re-185
76 - Os - 362 keV Os-192, also able to double beta decay. Of double beta stable isotopes, 1378 keV Os-190
77 - Ir - 1017 keV Ir-193
78 - Pt - 87 keV Pt-198, also able to double beta decay. Of double beta stable isotopes, 794 keV Pt-196
79 - Au - 954 keV Au-197
80 - Hg - alpha stable Hg-204 (the only such heavier than Dy-164) able to double beta decay. Of double beta stable isotopes, 136 keV Hg-202
81 - Tl - 157 keV Tl-205
82 - Pb - 391 keV Pb-391
83 - Bi - 3137 keV Bi-209

Looks like the bolded elements Hg to Pb form a stability island! All isotopes of all elements from 71 Lu to 75 Re release at least 1 MeV on alpha decay.
 
  • #9
Thinking aloud, I'd say that the theory should compose a probability of extracting two protons from the proton shell plus two neutrons from the neutron shell (the shells are nearby, of course, because of beta decay) and then the probability of crossing the barrier. This second prob should depend of Z and the total energy, while the former should depend of shell structure and thus both of Z,N.
 

1. What is alpha decay?

Alpha decay is a type of radioactive decay where an alpha particle (a helium nucleus consisting of two protons and two neutrons) is emitted from the nucleus of an atom. This process reduces the atomic number of the atom by two and the atomic mass by four.

2. How is the half-life of an isotope determined?

The half-life of an isotope is determined through experimental measurements. Scientists measure the rate at which the isotope decays and calculate the time it takes for half of the initial amount of the isotope to decay. This is known as the half-life.

3. What are notable light isotopes?

Notable light isotopes are isotopes that have a relatively low atomic mass compared to other isotopes of the same element. These isotopes are often used in scientific research and have important applications in various fields such as medicine and energy production.

4. How are estimates of alpha decay half-lives made?

Estimates of alpha decay half-lives are made using mathematical models and theoretical calculations based on the known properties of the isotope. These estimates are then compared to experimental data to validate their accuracy.

5. Why are there unknowns in the alpha decay half-lives of some isotopes?

There are unknowns in the alpha decay half-lives of some isotopes because not all isotopes have been extensively studied and measured. In addition, some isotopes may have very long half-lives, making it difficult to accurately measure their decay rate. Further research and experimentation are needed to determine the exact half-lives of these isotopes.

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