Question

Find the density of ${}_6^{12}C$ nucleus.

• A. $1g/c{m}^3$
• B. $1000kg/m^3$
• C. $2.4\times {10}^{16}kg/m^3$
• D. $1.4\times {10}^{17}kg/m^3$

Answer 1

Answer: (D)

$1.4\times {10}^{17}kg/m^3$

In one nucleus of ${}_6^{1}2C$ there are $6protons$ and $6Neutrons$

So mass of the above nucleus will be approximately $12m=12\times 1.67\times {10}^{-27}kg=2.004\times {10}^{-26}kg$

Where $m$ was the mass of a proton and it is also nearly equal to the mass of a neutron.

Radius of the above nucleus will be $R=1.2\times {10}^{-15}\times (A{)}^{1/3}meter$

Where $A=12$(Mass number)

Volume of the nucleus $V=\frac{4\pi R^3}{3}=4.1866R^3=4.1866\times {1.2}^3\times {10}^{-45}\times 12mete{r}^3=14.468\times {10}^{-44}{m}^3$

Dendity$=\frac{mass}{volume}=\frac{2.004}{14.468}{10}^{18}kg/m^3=1.4\times {10}^{17}kg/m^3$