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Nuclei — Physics STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 SciencePhysicsNuclei1 Mark
Question
For question, statements are given-one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer to these questions from the codes (a) (b) (c) and (d) as given below.
  1. Both A and R are true, and R is the correct explanation of A.
  2. Both A and R are true, but R is NOT the correct explanation of A.
  3. A is true, but R is false.
  4. A is false and R is also false.
Assertion (A): Density of all the nuclei is same.
Reason (R): Radius of nucleus is directly proportional to the cube root of mass number.
✓

Answer

  1. Both A and R are true, and R is the correct explanation of A.
Explanation:
Experimentally, it is found that the average radius of a nucleus is given by $\text{R}=\text{R}_0\text{A}\frac{1}{3}$ where $\text{R}_0=1.1\times10_{15}$and A = mass number
The volume of a nucleus is $\text{V}=\frac{4}{3}\pi\text{R}^3=\frac{4}{3}\pi\text{R}_0^3\text{A}$ Now as the masses of a proton and a neutron are roughly equal, say m, the mass of a nucleus is also roughly proportional to the mass number A, M = mA Hence density within a nucleus, $\rho=\frac{\text{M}}{\text{V}}-=\frac{\text{mA}}{\frac{4}{3}\pi\text{R}_0^3\text{A}}$
$=\frac{\text{m}}{\frac{4}{3}\pi\text{R}_0^3}$

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