SATHEE: Nuclei - Result Question 3

Nuclei - Result Question 3

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

(a) $1 : 3$

(b) $3 : 1$

(d) $1 : 1$

[2008]

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Answer:

Correct Answer: 3. (d)

Solution:

(d) Requird ratio of nuclear densities $= \frac{r_{1}}{r_{2}}$

$\begin{aligned} = \frac{(\frac{M_{1}}{V_{1}})}{(\frac{M_{2}}{V_{2}})} = \frac{M_{1}}{M_{2}} \times \frac{V_{2}}{V_{1}} = \frac{1}{3} \times \frac{\frac{4}{3} π R_{2}^{3}}{\frac{4}{3} π R_{1}^{3}} \\ = \frac{1}{3} \times (\frac{R_{2}}{R_{1}})^{3} = \frac{1}{3} \times (\frac{R_{0} M_{2}^{1 / 3}}{R_{0} M_{1}^{1 / 3}})^{3} [∴ R = R_{0} M^{1 / 3}] \end{aligned}$

$= \frac{1}{3} \times (\frac{M_{2}}{M_{1}}) = \frac{1}{3} \times (\frac{3}{1}) = 1 : 1$

Nuclear density, $ρ = \frac{3 m}{4 π R_{0}^{3}}$

Here, $R_{0} = 1.2 \times 10^{- 15} m m =$ Average of mass of a nuclean (mass of proton + mass of neutron) $= 1.66 \times 10^{- 27} k g$

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

Nuclei - Result Question 3

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

Answer:

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Nuclei - Result Question 3

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

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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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