Why is nuclear density the same for every nucleus? Also isotopes, isobars, isotones keep getting mixed in my head

6 answers & replies

• [+][–]Siddharth RaoDropperSample· 1mo ago

  Your arithmetic is fine and your reasoning is already the answer. Mass is proportional to $A$ (each nucleon has about the same mass). Volume is proportional to $R^3 = R_0^3A$, so also proportional to $A$. Ratio mass/volume is constant. What it tells you is that nucleons are packed at nearly constant density, like molecules in a drop of liquid, whether it's a small drop or a big one. That is why the liquid-drop model works.

  Your number: $\rho = \frac{1.66\times10^{-27}}{\frac43\pi(1.2\times10^{-15})^3}\approx 2.3\times10^{17}$ kg/m³. Matches NCERT.

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• [+][–]Harsh Gupta12thSample· 1mo ago

  Heavier nucleus has more mass in the same tiny space so obviously more density, uranium is denser than helium. Same logic as lead vs aluminium, heavier atom means denser stuff. I mean the nucleus is where all the mass sits, so more nucleons packed in must give more density. Simple 🙂

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  • [+][–]Tushar PawarDropperSample· 1mo ago

    That's atomic-scale thinking. Lead is denser than aluminium because the atoms are heavier and the atomic sizes are not growing as fast. In a nucleus the size grows exactly as the cube root of $A$, so volume tracks mass perfectly. Uranium nucleus isn't denser than a helium nucleus, they are nearly the same density. It's like comparing a litre of water with a swimming pool of water.

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    • [+][–]Lakshmi TripathiDropperSample· 1mo agoAuthor

      Pool and a glass of water, that comparison is good. Thank you, all of you. (Neutron stars have this density, I read, which is why they are so strange.)

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• [+][–]Pooja Iyer12thSample· 1mo ago

  Mnemonic time!! 🎵

  • Isotopes: same Z (same place in the periodic table, 'topos' = place). e.g. $^{35}$Cl and $^{37}$Cl.
  • Isobars: same mass number A ('bar' like barometer - weight). e.g. $^{40}$Ar and $^{40}$Ca.
  • Isotones: same number of neutrons, the n in tones. e.g. $^{14}$C ($N = 8$) and $^{15}$N ($N = 8$).

  (Bonus: isotones and neutrons both have an 'n' sound. dramatic but it works for me.)

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• [+][–]Vivek Mishra12thSample· 1mo ago

  For the ratio, use the formula directly. $R \propto A^{1/3}$, so

  $\frac{R_1}{R_2} = \left(\frac{8}{64}\right)^{1/3} = \left(\frac18\right)^{1/3} = \frac12$

  So 1:2, not 1:8. You took the ratio of volumes by mistake. Another easy one: $A = 27$ gives $R = 1.2\times3 = 3.6$ fm. Cube roots of 8, 27, 64, 125 are the usual numbers, so memorise them (2, 3, 4, 5).

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