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13.Nuclei
medium
Given the mass of iron nucleus as $55.85\,u$ and $A=56$, find the nuclear density?
A
$2.29 \times 10^{17} \;kg \;m ^{-3}$
B
$6.24 \times 10^{19} \;kg \;m ^{-3}$
C
$6.022 \times 10^{23} \;kg \;m ^{-3}$
D
$8.24 \times 10^{14} \;kg \;m ^{-3}$
Solution
$m_{ Fe }=55.85\,u =9.27 \times 10^{-26} \,kg$
Nuclear density $=\frac{\text { mass }}{\text { volume }}=\frac{9.27 \times 10^{-26}}{(4 \pi / 3)\left(1.2 \times 10^{-15}\right)^{3}} \times \frac{1}{56}$
$=2.29 \times 10^{17} \,kg \,m ^{-3}$
The density of matter in neutron stars (an astrophysical object) is comparable to this density. This shows that matter in these objects has been compressed to such an extent that they resemble a big nucleus.
Standard 12
Physics
