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प्रश्न
From the relation R = R0A1/3, where R0 is a constant and A is the mass number of a nucleus, show that the nuclear matter density is nearly constant (i.e. independent of A).
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उत्तर
We have the expression for nuclear radius as:
R = R0A1/3
Where,
R0 = Constant.
A = Mass number of the nucleus
Nuclear matter density, `rho = "Mass of the nucleus"/"Volume of the nucleus"`
Let m be the average mass of the nucleus.
Hence, mass of the nucleus = mA
`therefore rho = "mA"/(4/3 pi"R"^3) = "3mA"/(4pi ("R"_0 "A"^(1/3))^3) = (3"mA")/(4pi"R"_0^3 "A") = "3m"/(4pi"R"_0^3)`
Hence, the nuclear matter density is independent of A. It is nearly constant.
संबंधित प्रश्न
Answer the following question.
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Calculate approximately the ratio of the nuclear radii of the gold isotope \[_{79}^{197}Au\] and the silver isotope \[_{47}^{107}Ag\].
The mass number of He is 4 and that for sulphur is 32. The radius of sulphur nuclei is larger than that of helium by:
The Q value of a nuclear reaction A + b → C + d is defined by Q = [mA + mb − mC − md]c² where the masses refer to the respective nuclei. Calculate the Q-value of the reaction and state whether this reaction is exothermic or endothermic.
\[_1^1\mathrm{H}+_1^3\mathrm{H}\rightarrow_1^2\mathrm{H}+_1^2\mathrm{H}\]
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\[\mathrm{m(}_{1}^{1}\mathrm{H)}=1.007825\mathrm{u}\]
\[\mathrm{m(}_{1}^{2}\mathrm{H)}=2.014102\mathrm{u}\]
\[\mathrm{m(}_{1}^{3}\mathrm{H})=3.016049\mathrm{u}\]
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Reason (R): The size of the nucleus depends on atomic mass.
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