Show that nuclear density is independent of mass number

Asked by admin @ 11/08/2021 in Chemistry viewed by 327 People

How to show nuclear density is independent of mass number?

Answered by admin @ 11/08/2021

Nuclear density is independent of mass number.

Step by step explanation:

Let us consider,

Mass of nucleus = M

Volume of nucleus = V

Mass of nucleon = m

The formula of volume is as follows.

$V=\frac{4}{3}\pi\,r^{3}$ ..................(1)

The density of the molecule can be calculated by the following formula.

$\rho=\frac{M}{V}$ .................(2)

Substitute the equation (1) in equation (2) , then we get.

$M=\frac{4}{3}\pi r^{3}$ ....................(3)

We know $r=r_{o}A^{1/3}$

$r^{3}=r_{o}^{3}A$

Substitute the $r^{3}$ value in equation (3)

$M= \frac{4}{3}\pi r_{o}^{3}A \rho$ ......................(4)

Mass of nucleon m = mA.................(5)

Equating the 4 and 5 equations, then we get

$m=\frac{4}{3}\pi r_{o}^{3}\rho$

$\rho=\frac{3m}{4\pi r_{o}^{3}}$

From the above equation it is clearly shows nuclear density is independent on mass number.

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