Density of nuclear matter is nearly

Question

Density of nuclear matter is nearly (A)  1026 kg/m3  (B)  1024 kg/m3  (C)  1017 kg/m3  (D)  103 kg/m3

Tardigrade Admin · Accepted Answer

As we know that,
density of the nucleus

= \frac{mass of nucleus}{volume of nucleus}

Mass of the nucleus

= A \times 1.66 \times 1 0^{- 27} k g

,
where

A

is the mass number of nucleus.
Volume of the nucleus

= \frac{4}{3} π R^{3} = \frac{4}{3} π (R_{0} A^{1/3})^{3}

= \frac{4}{3} π R_{0}^{2} A

Thus, density

= \frac{A \times 1.66 \times 1 0 ^{- 27}}{( \frac{4}{3} π R _{0}^{3} ) A}

= \frac{1.66 \times 1 0 ^{- 27}}{( \frac{4}{3} π R _{0}^{3} )}

which shows that the density is independent of
mass number

A

Using,

R_{0} = 1.2 \times 1 0^{- 15} m

, we get
density

= 2.99 \times 1 0^{17} k g m^{- 3}

Q. Density of nuclear matter is nearly