Question:
Which one of the following is an example of doubly magic nuclei?
Which one of the following is an example of doubly magic nuclei?
Show Hint
Magic numbers are 2, 8, 20, 28, 50, 82, 126; find the nucleus where both Z and N are on the list.
Updated On: Aug 21, 2026
- \(^{18}\mathrm{O}\)
- \(^{48}\mathrm{Ca}\)
- \(^{124}\mathrm{Sn}\)
- \(^{204}\mathrm{Pb}\)
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The Correct Option is B
Solution and Explanation
Step 1: A nucleus is called magic when its proton number \(Z\) or neutron number \(N\) equals one of the shell-closure values. The magic numbers are \[2,\ 8,\ 20,\ 28,\ 50,\ 82,\ 126.\] A doubly magic nucleus has both \(Z\) and \(N\) equal to magic numbers, giving it exceptional stability.
Step 2: Evaluate each choice. For \(^{18}\mathrm{O}\): \(Z = 8\) (magic), \(N = 18 - 8 = 10\) (not magic). Only singly magic.
Step 3: For \(^{48}\mathrm{Ca}\): \(Z = 20\) (magic), \(N = 48 - 20 = 28\) (magic). Both are magic, so this is doubly magic.
Step 4: For \(^{124}\mathrm{Sn}\): \(Z = 50\) (magic), \(N = 124 - 50 = 74\) (not magic). Only singly magic. For \(^{204}\mathrm{Pb}\): \(Z = 82\) (magic), \(N = 204 - 82 = 122\) (not magic, the magic value here would be \(126\), i.e. \(^{208}\mathrm{Pb}\)). Only singly magic.
Step 5: Only \(^{48}\mathrm{Ca}\) has both numbers magic, so option (B) is correct.
\[\boxed{^{48}\mathrm{Ca}}\]
Step 2: Evaluate each choice. For \(^{18}\mathrm{O}\): \(Z = 8\) (magic), \(N = 18 - 8 = 10\) (not magic). Only singly magic.
Step 3: For \(^{48}\mathrm{Ca}\): \(Z = 20\) (magic), \(N = 48 - 20 = 28\) (magic). Both are magic, so this is doubly magic.
Step 4: For \(^{124}\mathrm{Sn}\): \(Z = 50\) (magic), \(N = 124 - 50 = 74\) (not magic). Only singly magic. For \(^{204}\mathrm{Pb}\): \(Z = 82\) (magic), \(N = 204 - 82 = 122\) (not magic, the magic value here would be \(126\), i.e. \(^{208}\mathrm{Pb}\)). Only singly magic.
Step 5: Only \(^{48}\mathrm{Ca}\) has both numbers magic, so option (B) is correct.
\[\boxed{^{48}\mathrm{Ca}}\]
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