I am given the following question:

228-88 Ra is an isotope of Radium.

A-Z Ra is a neutral atom of a different isotope of radium. State the possible value for A and Z.

The value for Z is 88 because the proton number is the same between isotopes.

According to the mark scheme, the value for A is 228 +- 10, but I don't know why.

My uneducated intuition told me this means there are 20 other isotopes of Radium: 10 with nucleon numbers incrementing from 229-238, and 10 from 227-218.

However, according to the table of nuclides, there are only two other isotopes of Radium with a nucleon number above 228 (229 and 230).

This means that anything above 228+2 would be wrong, but they have given +10.

What am I missing?

  • 1
    $\begingroup$ Wikipedia gives even more: 202 to 234. en.m.wikipedia.org/wiki/Isotopes_of_radium $\endgroup$ – badjohn Mar 27 at 18:17
  • $\begingroup$ I've added the homework-and-exercises tag. In the future, please use this tag on this type of question. $\endgroup$ – Ben Crowell Mar 27 at 18:24
  • $\begingroup$ @badjohn The biggest one there is still only +7 $\endgroup$ – Gerard Way Mar 27 at 18:43
  • $\begingroup$ I suspect that you have been given some heuristics on, given Z, how broad a range of A one might suspect. $\endgroup$ – Jon Custer Mar 27 at 18:51
  • $\begingroup$ Yes but more than you were expecting. It seems that the example is towards the heavier end of the range. $\endgroup$ – badjohn Mar 27 at 19:18

I don't know where you are getting your numbers but you should check a Chart of the Nuclides. There are more than 20 isotopes of Radium. Maybe not 10 more than 228 but more than 20 total. The 2 you found were maybe the stable ones but others exist as well. Your reasoning is right-on you just need the correct numbers to back you up.

The chart of the nuclides contains a large amount of data. The online version of the chart is tedious but contains all the info you need.

  • $\begingroup$ The OP is talking about radium, not radon, but I suppose you actually meant radium. But anyway, both elements are radioactive, with no stable isotopes. The most stable radium isotope, $^{226}$Ra, has a halflife of 1600 years. $\endgroup$ – PM 2Ring Mar 28 at 5:10
  • $\begingroup$ Yes, I meant radium. Sorry about that and thanks for pointing out my mistake. I'll correct it now. $\endgroup$ – jmh Mar 28 at 15:13

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