InterviewSolution
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InterviewSolution
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How does radius of a nucleus vary with mass number ? Show that nuclear density is the same for all nuclei. |
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Answer» <P> The dimensions of nucleus have been measured by several experiments involving the scattering of N, p, `alpha`-particle etc. Every time it is found that the VOLUME of nucleus is directly proportional to the number of NUCLEONS (A) in the nucleus. If R is the radius of the nucleus having mass number A, then `4/3 pi R^(3) prop A` or `R^(3) prop A` or `R prop A^(1//3)` or `R=A_(0)A^(1//3)` where `R_(0)=1.2xx10^(-15)m=1.2` fm. It shows that GREATER the mass number, greater the nuclear radius. Density of nucleus `(rho)`. It is defined as the nuclear mass per unit volume. i.e. `rho=("Mass of nucleus")/("Volume of nucleus")` `=("Mass of one nucleon" xx "Number of nucleons")/(4/3 pi r^(3))` `=(1.66xx10^(-17)A)/(4/3 pi (R_(0)A^(1//3))^(3))` `=(3 xx 1.66 xx 10^(-27)A)/(4xx3.142xx(1.2xx10^(-15))^(3)xxA)` `=2.29xx10^(17)"kg m"^(-3)` Thus the nuclear density is of the order of `10^(17)` kg `m^(-3)` and independent of its mass number. Therefore, all nuclei have the same approximate density. |
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