Ncert Exercises & Solutions

The unit of length convenient on the nuclear scale is a fermi: $1 f = 10^{- 15} m .$ Nuclear sizes obey roughly the following empirical relation:

$𝑟 = 𝑟_{0} 𝐴^{1 / 3}$

where r is the radius of the nucleus, A its mass number, and r0 is a constant equal to about, 1.2 f. Show that the rule implies that nuclear mass density is nearly constant for different nuclei. Estimate the mass density of the sodium nucleus. Compare it with the average mass density of a sodium atom obtained in Exercise. 2.27.

Let m is the average mass of proton or nucleon
Therefore Nuclear mas'

M=mA

A n d r a d i u s o f n u c l e u s, r = r_{0} A^{1 / 3}

N u c l e a r d e n s i t y, ρ = \frac{m A}{\frac{4}{3} π {(r_{0} A^{1 / 3})}^{3}} = \frac{3 m}{4 π {r_{0}}^{3}}

\Rightarrow ρ = \frac{3 \times 1.66 \times 10^{- 27}}{4 \times 3.14 \times {(1.2 \times 10^{- 15})}^{3}}

= 2.29 \times 10^{17} k g m^{- 3}

F r o m l a s t q u e s t i o n 2.27, d e n s i t y o f s o d i u m a t o m = 0.58 \times 10^{3} k g m^{- 3}

\Rightarrow \frac{N u c l e a r m a s s d e n s i t y}{A t o m i c m a s s d e n s i t y} = \frac{2.30 \times 10^{17}}{0.58 \times 10^{3}} = 3.96 \times 10^{14}

Therefore Nuclear density is around

10^{15}

times the atomic density of matter.

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