NEET-XII-Physics
46: The Nucleus
- #1Assume that the mass of a nucleus is approximately given by M = Amp where A is the mass number. Estimate the density of matter in kgm-3 inside a nucleus. What is the specific gravity of nuclear matter?Ans : Given:
Mass of the nucleus, M = Amp
Volume of the nucleus, V = `` \frac{4}{3}\pi {{R}_{0}}^{3}A``
Density of the matter, `` d=\frac{M}{V}=\frac{A{m}_{p}}{{\displaystyle \frac{4}{3}}\pi {{R}_{0}}^{3}A}``
`` =\frac{3{m}_{p}}{4\times \pi {{R}_{0}}^{3}}``
`` =\frac{3\times 1.007276}{4\times 3.14(1.1{)}^{3}}``
`` =3\times {10}^{17}\,\mathrm{\,kg\,}/{\,\mathrm{\,m\,}}^{3}``
Specific gravity of the nuclear matter = `` \frac{\,\mathrm{\,Density\,}\,\mathrm{\,of\,}\,\mathrm{\,matter\,}}{\,\mathrm{\,Density\,}\,\mathrm{\,of\,}\,\mathrm{\,water\,}}``
`` \therefore `` Specific gravity = `` \frac{3\times {10}^{17}}{{10}^{3}}`` = 3 `` \times `` 1014 kg/m3
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