Why is Technetium (Element 43) radioactive?

[WCOLtd]

It seems odd to me that there would be a radioactive atom so far up the periodic table. What is it about this atom's atomic nucleus that makes it so unstable?

 

[fresh_42]

According to the liquid-drop-model of nuclei the most stable isotope would be 100-Tc. But with two odd numbers of protons (43) and neutrons (57) it could only be stable if there weren't other stable nuclei with two even numbers of protons and neutrons, which are 100-Mo (42/58) and 100-Ru (44/56). The second is stable and the first almost $(7.3 \cdot 10^{18}a)$. (Also a consequence of this model, however, I haven't found a short way to see it.)
Thus the heavy isotopes decay per neutron emission and the lighter per electron capture.

 

[mfb]

Did you check the Wikipedia page? It has a good introduction. There are several factors, mainly the very low energy of nuclei of elements nearby combined with the odd number of protons of technetium.

 

[fresh_42]

Did you check the Wikipedia page? It has a good introduction. There are several factors, mainly the very low energy of nuclei of elements nearby combined with the odd number of protons of technetium.

I have taken the German one and wrote a kind of summarization. Unfortunately the English site wasn't as detailed concerning the radioactivity of the isotopes. The good thing is, I learned something about the stability of nuclei myself.

Edit: the 100-Tc was a result from a formula on the liquid-drop-model page plus Wolfram.

 

[mathman]

It seems odd to me that there would be a radioactive atom so far up the periodic table. What is it about this atom's atomic nucleus that makes it so unstable?

All (?) elements have radioactive isotopes.

It seems odd to me that there would be a radioactive atom so far up the periodic table. What is it about this atom's atomic nucleus that makes it so unstable?

All (?) elements have radioactive isotopes. What is unusual is that elements 43 and 61 are the only elements with atomic number < 82 that have no stable isotope.

 

[snorkack]

Is it pure random chance that elements 43 and 61 don't have any stable isotopes, or is there any more reason?
From elements 1 to 16, every element has exactly 1 stable odd isotope. Starting with 17, the pattern gets more random:
17: 2 - 35, 37
18: 0
19: 2 - 39, 41
20: 1 - 43
21: 1 - 45
22: 2 - 47, 49
23: 1 - 51
24: 1 - 53
25: 1 - 55
26: 1 - 57
27: 1 - 59
28: 1 - 61
29: 2 - 63, 65
30: 1 - 67
31: 2 - 69, 71
32: 1 - 73
33: 1 - 75
34: 1 - 77
35: 1 - 79, 81
36: 1 - 83
37: 1 - 85
38: 1 - 87
39: 1 - 89
40: 1 - 91
41: 1 - 93
42: 2 - 95, 97
43: 0
44: 2 - 99, 101
45: 1 - 103
46: 1 - 105
47: 2 - 107, 109
48: 1 - 111
49: 1 - 113
50: 3 - 115, 117, 119
51: 2 - 121, 123
52: 1 - 125
53: 1 - 127
54: 2 - 129, 131
55: 1 - 133
56: 2 - 135, 137
57: 1 - 139
58: 0
59: 1 - 141
60: 2 - 143, 145
61: 0
62: 2 - 147, 149
63: 2 - 151, 153
64: 2 - 155, 157
65: 1 - 159
66: 2 - 161, 163
67: 1 - 165
68: 1 - 167
69: 1 - 169
70: 2 - 171, 173
71: 1 - 175
72: 2 - 177, 179
73: 1 - 181
74: 1 - 183
75: 1 - 185
76: 2 - 187, 189
77: 2 - 191, 193
78: 1 - 195
79: 1 - 197
80: 2 - 199, 201
81: 2 - 203, 205
82: 1 - 207
83: 1 - 209.

The absence of stable odd isotopes of elements 18 and 58 is just as odd as their absence for elements 43 and 61.

 

[fresh_42]

Is it pure random chance that elements 43 and 61 don't have any stable isotopes, or is there any more reason?

As far as I can see it, the liquid-drop-model is - as quoted - semi-empirical, i.e. it takes the observations and tries to explain them by patterns. Those patterns represent the more general principle, that nature always tries to find local energy minima, stable points of balance where energy from elsewhere is needed to leave those states. Since all three atomic forces play a role here the overall situation can be pretty complex. The patterns mentioned in the liquid-drop-model are meant to reduce this complexity onto computational principles. And it works astonishingly well as I experienced as I took them to calculate 100-Tc as a preferred state.

 

[mfb]

The absence of stable odd isotopes of elements 18 and 58 is just as odd as their absence for elements 43 and 61.

All the odd isotopes argon. scnr.

It is not that odd for the even-numbered elements - ³⁷Ar would have 19 neutrons, ³⁹Ar would have 21 neutrons. 20 is a magic number (the nuclear equivalent of noble gases - completed shells), so ³⁷Cl and ³⁹K are strongly bound, and the argon isotopes decay to those.

¹³⁹Ce has 81 neutrons, ¹⁴¹ has 83. And 82 is a magic number again.

While the Wikipedia page about technetium is a bit short, the linked article isotopes of technetium has more details.

Magic numbers for reference: 2, 8, 20, 28, 50, 82, and 126

 

[snorkack]

It is not that odd for the even-numbered elements - ³⁷Ar would have 19 neutrons, ³⁹Ar would have 21 neutrons. 20 is a magic number (the nuclear equivalent of noble gases - completed shells), so ³⁷Cl and ³⁹K are strongly bound, and the argon isotopes decay to those.

¹³⁹Ce has 81 neutrons, ¹⁴¹ has 83. And 82 is a magic number again.

Magic numbers for reference: 2, 8, 20, 28, 50, 82, and 126

Then why are 55 and 85 the preferred neutron numbers, seeing how both are odd?

 

[mfb]

Preferred in which way, and where do those numbers come from?

Cerium has the most stable isotope at 82 neutrons, 78, 80 and 84 neutrons also lead to isotopes without observed decay.

 

[snorkack]

Preferred in which way, and where do those numbers come from?

Technetium has no stable isotope because both 97 and 99 are unstable. For 97, the stable isobar is Mo, with 55 neutrons. For 99, the stable isobar is Ru, also with 55 neutrons. What´s special about 55 neutrons?
Promethium has no stable isotopes because both 145 and 147 are unstable. For 145, the stable isobar is Nd, with 85 neutrons. For 147, the stable isobar is Sm, also with 85 neutrons.

 

[mfb]

It's not the 55 neutrons, it's the paired 42 and 44 protons. There can be only one stable isotope with an odd sum of protons and neutrons, in both cases the elements nearby have a slightly lower energy. Same for promethium.

 

[snorkack]

It's not the 55 neutrons, it's the paired 42 and 44 protons. There can be only one stable isotope with an odd sum of protons and neutrons, in both cases the elements nearby have a slightly lower energy.

Are 43 and 44 then both magic numbers?

 

[mfb]

None of them is magic, see above. But paired protons and neutrons in general lead to lower energies, and in this case the paired protons win by a small margin.

 

[WCOLtd]

Thank you for the replies I especially learned much about the liquid drop model. Very useful explanation.