Nuclei - Result Question 2

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2. If the nuclear radius of ${ }^{27} Al$ is 3.6 Fermi, the approximate nuclear radius of ${ }^{64} Cu$ in Fermi is :

======= ####2. If the nuclear radius of ${ }^{27} Al$ is 3.6 Fermi, the approximate nuclear radius of ${ }^{64} Cu$ in Fermi is :

3e0f7ab6f6a50373c3f2dbda6ca2533482a77bed:content/english/neet-pyq-chapterwise/physics/nuclei/nuclei—result-question-2.md (a) 2.4

(b) 1.2

(c) 4.8

(d) 3.6

[2012]

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Answer:

Correct Answer: 2. (c)

Solution:

  1. (c) The radius of the nuclears is directly proportional to cube root of atomic number i.e. $R \propto A^{1 / 3}$

$R=R_0 A^{1 / 3}$, where $R_0$ is a constant of proportionality

$\frac{R_2}{R_1}=(\frac{A_2}{A_1})^{1 / 3} \Rightarrow(\frac{64}{27})^{1 / 3}=\frac{4}{3}$

where $R_1=$ the radius of ${ }^{27} Al$, and $A_1=$ Atomic mass number of $A 1$

$R_2=$ the radius of ${ }^{64} Cu$ and $A_2=$ Atomic mass number of $C 4$

$ R_2=3.6 \times \frac{4}{3}=4.8 m $