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As the Mass Number a Increases, Which of the Following Quantities Related to a Nucleus Do Not Change? - Physics

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Question

As the mass number A increases, which of the following quantities related to a nucleus do not change?

  • Mass

  • Volume

  • Density

  • Binding energy

Solution

Density

Radius of a nucleus with mass number A is given as `R = R_0A^1"/"3`

Here, Ro = 1.2 fm

therefore Volume of the nucleus = `(4piR^3)/3 = (4piR_0^3A)/3`

This depends on A. With an increase in A, V increases proportionally.
Mass of the nucleus \[\simeq\] AmN

Here, mN is the mass of a nucleon.
Therefore, mass of the nucleus also increases with the increasing mass number.
Binding energy also depends on mass number (number of nucleons) as it is the difference between the total mass of the constituent nucleons and the nucleus. Therefore, it also varies with the changing mass number.

On the other hand,

`Density = "Mass"/"Volume" = (Am_N)/(4piR^3"/"3) = (Am_N)/(4piR_0^3A"/"3) = (m_N)/(4piR_0^3"/"3) = (3m_N)/(4piR_0^3)`

This is independent of A and hence does not change as mass number increases.

  Is there an error in this question or solution?

APPEARS IN

 HC Verma Solution for Concepts of Physics - Vol. 2 (2018 to Current)
Chapter 24: The Nucleus
MCQ | Q: 1 | Page no. 441
Solution As the Mass Number a Increases, Which of the Following Quantities Related to a Nucleus Do Not Change? Concept: Nuclear Energy - Fission.
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