The unit of length convenient on the nuclear scale

Asked by admin @ 23/08/2021 in Physics viewed by 246 People

Question 2.28 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=r0* 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 sodium nucleus. Compare it with the average mass density of a sodium atom obtained in Exercise. 2.27.
Chapter Units And Measurements Page 37

Answered by admin @ 23/08/2021

Q5.
r = r°A⅓
Where r is the radius of nuclues
And A is the mass number .
Volume of nuclues = 4/3 π r³
= 4/3 π ( r°A⅓)³ = 4πr°³A/3

Now,
Mass of nuclues = mass number × 1/Avogadro's constant
= A × 10^-3 /Na { Na is Avogadro's constant }
Density of nuclues = M/V = A× 10^-3/Na{4πr°³A/3}
= 3× 10^-3/Na×4πr°³ e.g constant
Hence proved //

Average mass density of sodium atom = 3× 10^-3/Na × 4πr°³
= 3× 10^-3 /{ 6.023 × 10^23 × 4 × 3.14 × (1.2 × 10^-15)³ } Kg/m³
= 2.29 × 10^17 Kg/m³

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The unit of length convenient on the nuclear scale

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