Nuclear density of hydrogen is 2.3x1017 kg/m3. Given A = 56 for iron, find its nuclear density

Asked by gaurish6247 | 7th Apr, 2021, 05:16: PM

Expert Answer:

Radius of Hydrogen  nucleus, RH = Ro A1/3 = Ro
 
Where A is Mass number
 
Radius of Fe nucleus  RFe = Ro 561/3
 
Density of hydrogen nuclei , begin mathsize 14px style rho subscript H end style = mass / volume =  mH / [ (4/3)π RH3 ]
 
Density of Fe nuclei , begin mathsize 14px style rho subscript F e end subscript end style = mFe / [ (4/3)π RFe3 ]
 
begin mathsize 14px style rho subscript H over rho subscript F e end subscript space equals space m subscript H over m subscript F e end subscript cross times fraction numerator R subscript F e end subscript superscript 3 over denominator R subscript H superscript 3 end fraction space equals space 1 over 56 cross times begin inline style 56 over 1 end style space equals space 1 end style
Density of Fe nucleus and Density of Hydrogen nucleus are same
 
begin mathsize 14px style rho subscript H end style = begin mathsize 14px style rho subscript F e end subscript end style = 2.3 × 1017 kg/m3

Answered by Thiyagarajan K | 7th Apr, 2021, 10:11: PM