Nuclei - Result Question 3

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3. Two nuclei have their mass numbers in the ratio of $1: 3$. The ratio of their nuclear densities would be

======= ####3. Two nuclei have their mass numbers in the ratio of $1: 3$. The ratio of their nuclear densities would be

3e0f7ab6f6a50373c3f2dbda6ca2533482a77bed:content/english/neet-pyq-chapterwise/physics/nuclei/nuclei—result-question-3.md (a) $1: 3$

(b) $3: 1$

(c) $(3)^{1 / 3}: 1$

(d) $1: 1$

[2008]

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Answer:

Correct Answer: 3. (d)

Solution:

  1. (d) Requird ratio of nuclear densities $=\frac{r_1}{r_2}$

$ \begin{aligned} & =\frac{(\frac{M_1}{V_1})}{(\frac{M_2}{V_2})}=\frac{M_1}{M_2} \times \frac{V_2}{V_1}=\frac{1}{3} \times \frac{\frac{4}{3} \pi R_2^{3}}{\frac{4}{3} \pi R_1^{3}} \\ & =\frac{1}{3} \times(\frac{R_2}{R_1})^{3}=\frac{1}{3} \times(\frac{R_0 M_2^{1 / 3}}{R_0 M_1^{1 / 3}})^{3}[\therefore R=R_0 M^{1 / 3}] \end{aligned} $

$=\frac{1}{3} \times(\frac{M_2}{M_1})=\frac{1}{3} \times(\frac{3}{1})=1: 1$

Nuclear density, $\rho=\frac{3 m}{4 \pi R_0^{3}}$

Here, $R_0=1.2 \times 10^{-15} m m=$ Average of mass of a nuclean (mass of proton + mass of neutron) $=1.66 \times 10^{-27} kg$

This formula suggest that density of nuclear matter is same for all nuclei.