# Isotopes of calcium

Calcium ($_{20}$Ca) has 26 known isotopes, ranging from $^{35}$Ca to $^{60}$Ca. There are five stable isotopes ($^{40}$Ca, $^{42}$Ca, $^{43}$Ca, $^{44}$Ca and $^{46}$Ca), plus one isotope ($^{48}$Ca) with such a long half-life that it is for all practical purposes stable. The most abundant isotope, $^{40}$Ca, as well as the rare $^{46}$Ca, are theoretically unstable on energetic grounds, but their decay has not been observed. Calcium also has a cosmogenic isotope, $^{41}$Ca, with half-life 99,400 years. Unlike cosmogenic isotopes that are produced in the air, $^{41}$Ca is produced by neutron activation of $^{40}$Ca. Most of its production is in the upper metre of the soil column, where the cosmogenic neutron flux is still strong enough. $^{41}$Ca has received much attention in stellar studies because it decays to $^{41}$K, a critical indicator of solar system anomalies. The most stable artificial isotopes are $^{45}$Ca with half-life 163 days and $^{47}$Ca with half-life 4.5 days. All other calcium isotopes have half-lives of minutes or less.
Stable $^{40}$Ca comprises about 97% of natural calcium and is mainly created by nucleosynthesis in large stars. Similarly to $^{40}$Ar, however, some atoms of $^{40}$Ca are radiogenic, created through the radioactive decay of $^{40}$K. While K–Ar dating has been used extensively in the geological sciences, the prevalence of $^{40}$Ca in nature initially impeded the proliferation of K-Ca dating in early studies, with only a handful of studies in the 20th century. Modern techniques using increasingly precise Thermal-Ionization (TIMS) and Collision-Cell Multi-Collector Inductively-coupled plasma mass spectrometry (CC-MC-ICP-MS) techniques, however, have been used for successful K–Ca age dating, as well as determining K losses from the lower continental crust and for source-tracing calcium contributions from various geologic reservoirs similar to Rb-Sr.
Stable isotope variations of calcium (most typically $^{44}$Ca/$^{40}$Ca or $^{44}$Ca/$^{42}$Ca, denoted as 'δ$^{44}$Ca' and 'δ$^{44/42}$Ca' in delta notation) are also widely used across the natural sciences for a number of applications, ranging from early determination of osteoporosis to quantifying volcanic eruption timescales. Other applications include: quantifying carbon sequestration efficiency in CO$_2$ injection sites and understanding ocean acidification, exploring both ubiquitous and rare magmatic processes, such as formation of granites and carbonatites, tracing modern and ancient trophic webs including in dinosaurs, assessing weaning practices in ancient humans, and a plethora of other emerging applications.

## List of isotopes

| Nuclide | Z | N | Isotopic mass (Da) | Half-life | Decay mode | Daughter isotope | Spin and parity | Natural abundance (mole fraction) | Natural abundance (mole fraction) |
| Nuclide | Z | N | Isotopic mass (Da) | Half-life | Decay mode | Daughter isotope | Spin and parity | Normal proportion | Range of variation |
| $^{35}$Ca | 20 | 15 | 35.00557(22)# | 25.7(2) ms | β$^+$, p (95.8%) | $^{34}$Ar | 1/2+# | | |
| $^{35}$Ca | 20 | 15 | 35.00557(22)# | 25.7(2) ms | β$^+$, 2p (4.2%) | $^{33}$Cl | 1/2+# | | |
| $^{35}$Ca | 20 | 15 | 35.00557(22)# | 25.7(2) ms | β$^+$ (rare) | $^{35}$K | 1/2+# | | |
| $^{36}$Ca | 20 | 16 | 35.993074(43) | 100.9(13) ms | β$^+$, p (51.2%) | $^{35}$Ar | 0+ | | |
| $^{36}$Ca | 20 | 16 | 35.993074(43) | 100.9(13) ms | β$^+$ (48.8%) | $^{36}$K | 0+ | | |
| $^{37}$Ca | 20 | 17 | 36.98589785(68) | 181.0(9) ms | β$^+$, p (76.8%) | $^{36}$Ar | 3/2+ | | |
| $^{37}$Ca | 20 | 17 | 36.98589785(68) | 181.0(9) ms | β$^+$ (23.2%) | $^{37}$K | 3/2+ | | |
| $^{38}$Ca | 20 | 18 | 37.97631922(21) | 443.70(25) ms | β$^+$ | $^{38}$K | 0+ | | |
| $^{39}$Ca | 20 | 19 | 38.97071081(64) | 860.3(8) ms | β$^+$ | $^{39}$K | 3/2+ | | |
| $^{40}$Ca | 20 | 20 | 39.962590850(22) | Observationally stable | Observationally stable | Observationally stable | 0+ | 0.9694(16) | 0.96933–0.96947 |
| $^{41}$Ca | 20 | 21 | 40.96227791(15) | 9.94(15)×10$^4$ y | EC | $^{41}$K | 7/2− | Trace | |
| $^{42}$Ca | 20 | 22 | 41.95861778(16) | Stable | Stable | Stable | 0+ | 0.00647(23) | 0.00646–0.00648 |
| $^{43}$Ca | 20 | 23 | 42.95876638(24) | Stable | Stable | Stable | 7/2− | 0.00135(10) | 0.00135–0.00135 |
| $^{44}$Ca | 20 | 24 | 43.95548149(35) | Stable | Stable | Stable | 0+ | 0.0209(11) | 0.02082–0.02092 |
| $^{45}$Ca | 20 | 25 | 44.95618627(39) | 162.61(9) d | β$^−$ | $^{45}$Sc | 7/2− | | |
| $^{46}$Ca | 20 | 26 | 45.9536877(24) | Observationally stable | Observationally stable | Observationally stable | 0+ | 4×10$^{−5}$ | 4×10$^{−5}$–4×10$^{−5}$ |
| $^{47}$Ca | 20 | 27 | 46.9545411(24) | 4.536(3) d | β$^−$ | $^{47}$Sc | 7/2− | | |
| $^{48}$Ca | 20 | 28 | 47.952522654(18) | 5.6(10)×10$^{19}$ y | β$^−$β$^−$ | $^{48}$Ti | 0+ | 0.00187(21) | 0.00186–0.00188 |
| $^{49}$Ca | 20 | 29 | 48.95566263(19) | 8.718(6) min | β$^−$ | $^{49}$Sc | 3/2− | | |
| $^{50}$Ca | 20 | 30 | 49.9574992(17) | 13.45(5) s | β$^−$ | $^{50}$Sc | 0+ | | |
| $^{51}$Ca | 20 | 31 | 50.96099566(56) | 10.0(8) s | β$^−$ | $^{51}$Sc | 3/2− | | |
| $^{51}$Ca | 20 | 31 | 50.96099566(56) | 10.0(8) s | β$^−$, n? | $^{50}$Sc | 3/2− | | |
| $^{52}$Ca | 20 | 32 | 51.96321365(72) | 4.6(3) s | β$^−$ (>98%) | $^{52}$Sc | 0+ | | |
| $^{52}$Ca | 20 | 32 | 51.96321365(72) | 4.6(3) s | β$^−$, n (<2%) | $^{51}$Sc | 0+ | | |
| $^{53}$Ca | 20 | 33 | 52.968451(47) | 461(90) ms | β$^−$ (60%) | $^{53}$Sc | 1/2−# | | |
| $^{53}$Ca | 20 | 33 | 52.968451(47) | 461(90) ms | β$^−$, n (40%) | $^{52}$Sc | 1/2−# | | |
| $^{54}$Ca | 20 | 34 | 53.972989(52) | 90(6) ms | β$^−$ | $^{54}$Sc | 0+ | | |
| $^{54}$Ca | 20 | 34 | 53.972989(52) | 90(6) ms | β$^−$, n? | $^{53}$Sc | 0+ | | |
| $^{54}$Ca | 20 | 34 | 53.972989(52) | 90(6) ms | β$^−$, 2n? | $^{52}$Sc | 0+ | | |
| $^{55}$Ca | 20 | 35 | 54.97998(17) | 22(2) ms | β$^−$ | $^{55}$Sc | 5/2−# | | |
| $^{55}$Ca | 20 | 35 | 54.97998(17) | 22(2) ms | β$^−$, n? | $^{54}$Sc | 5/2−# | | |
| $^{55}$Ca | 20 | 35 | 54.97998(17) | 22(2) ms | β$^−$, 2n? | $^{53}$Sc | 5/2−# | | |
| $^{56}$Ca | 20 | 36 | 55.98550(27) | 11(2) ms | β$^−$ | $^{56}$Sc | 0+ | | |
| $^{56}$Ca | 20 | 36 | 55.98550(27) | 11(2) ms | β$^−$, n? | $^{55}$Sc | 0+ | | |
| $^{56}$Ca | 20 | 36 | 55.98550(27) | 11(2) ms | β$^−$, 2n? | $^{54}$Sc | 0+ | | |
| $^{57}$Ca | 20 | 37 | 56.99296(43)# | 8# ms [>620 ns] | β$^−$? | $^{57}$Sc | 5/2−# | | |
| $^{57}$Ca | 20 | 37 | 56.99296(43)# | 8# ms [>620 ns] | β$^−$, n? | $^{56}$Sc | 5/2−# | | |
| $^{57}$Ca | 20 | 37 | 56.99296(43)# | 8# ms [>620 ns] | β$^−$, 2n? | $^{55}$Sc | 5/2−# | | |
| $^{58}$Ca | 20 | 38 | 57.99836(54)# | 4# ms [>620 ns] | β$^−$? | $^{58}$Sc | 0+ | | |
| $^{58}$Ca | 20 | 38 | 57.99836(54)# | 4# ms [>620 ns] | β$^−$, n? | $^{57}$Sc | 0+ | | |
| $^{58}$Ca | 20 | 38 | 57.99836(54)# | 4# ms [>620 ns] | β$^−$, 2n? | $^{56}$Sc | 0+ | | |
| $^{59}$Ca | 20 | 39 | 59.00624(64)# | 5# ms [>400 ns] | β$^−$? | $^{59}$Sc | 5/2−# | | |
| $^{59}$Ca | 20 | 39 | 59.00624(64)# | 5# ms [>400 ns] | β$^−$, n? | $^{58}$Sc | 5/2−# | | |
| $^{59}$Ca | 20 | 39 | 59.00624(64)# | 5# ms [>400 ns] | β$^−$, 2n? | $^{57}$Sc | 5/2−# | | |
| $^{60}$Ca | 20 | 40 | 60.01181(75)# | 2# ms [>400 ns] | β$^−$? | $^{60}$Sc | 0+ | | |
| $^{60}$Ca | 20 | 40 | 60.01181(75)# | 2# ms [>400 ns] | β$^−$, n? | $^{59}$Sc | 0+ | | |
| $^{60}$Ca | 20 | 40 | 60.01181(75)# | 2# ms [>400 ns] | β$^−$, 2n? | $^{58}$Sc | 0+ | | |
| This table header & footer: view ||||||||||
* ↑ ( ) – Uncertainty (1σ) is given in concise form in parentheses after the corresponding last digits.
* ↑ Bold half-life – nearly stable, half-life longer than age of universe.
* ↑ Modes of decay: EC:Electron capture n:Neutron emission p:Proton emission
* ↑ Bold symbol as daughter – Daughter product is stable.
* ↑ ( ) spin value – Indicates spin with weak assignment arguments.
* ↑ # – Values marked # are not purely derived from experimental data, but at least partly from trends of neighboring nuclides (TNN).
* ↑ Heaviest observationally stable nuclide with equal numbers of protons and neutrons
* ↑ Believed to undergo double electron capture to $^{40}$Ar with a half-life no less than 9.9×10$^{21}$ y
* ↑ Cosmogenic nuclide
* ↑ Believed to undergo β$^−$β$^−$ decay to $^{46}$Ti
* ↑ Primordial radionuclide
* ↑ Believed to be capable of undergoing triple beta decay with very long partial half-life
* ↑ Lightest nuclide known to undergo double beta decay
* ↑ Theorized to also undergo β$^−$ decay to $^{48}$Sc with a partial half-life exceeding 1.1$^{+0.8}$ $_{−0.6}$×10$^{21}$ years

## Calcium-48

Calcium-48 is a doubly magic nucleus with 28 neutrons; unusually neutron-rich for a light primordial nucleus. It decays via double beta decay with an extremely long half-life of about 6.4×10$^{19}$ years, though single beta decay is also theoretically possible. This decay can analyzed with the sd nuclear shell model, and it is more energetic (4.27 MeV) than any other double beta decay. It can also be used as a precursor for neutron-rich and superheavy nuclei.

## Calcium-60

Calcium-60 is the heaviest known isotope as of 2020. First observed in 2018 at Riken alongside $^{59}$Ca and seven isotopes of other elements, its existence suggests that there are additional even-N isotopes of calcium up to at least $^{70}$Ca, while $^{59}$Ca is probably the last bound isotope with odd N. Earlier predictions had estimated the neutron drip line to occur at $^{60}$Ca, with $^{59}$Ca unbound.
In the neutron-rich region, N = 40 becomes a magic number, so $^{60}$Ca was considered early on to be a possibly doubly magic nucleus, as is observed for the $^{68}$Ni isotone. However, subsequent spectroscopic measurements of the nearby nuclides $^{56}$Ca, $^{58}$Ca, and $^{62}$Ti instead predict that it should lie on the island of inversion known to exist around $^{64}$Cr.