Size and Density | Nuclear and Particle Physics for GATE - GATE Physics PDF Download

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1(b). Size and Density 
 Majority of atomic nuclei have spherical shape and only very few show departure from 
spherical symmetry. For spherically symmetrical nuclei, nuclear radius is given by   
                                                         
1/ 3
0
R R A ? 
where A is the mass number and ? ?
15
0
1.2 0.1 10 1.2 R m fm
?
? ? ? ? .  
R varies slightly from one nucleus to another but is roughly constant for 20 A ? . 
The radius of 
12
6
C nucleus is  
                                                ? ? ? ? fm R 7 . 2 12 2 . 1
3 / 1
? ? 
Example: The radius of Ge nucleus is measured to be twice the radius of
9
4
Be . How 
many nucleons are there in Ge
 
nucleus?  
Solution: ? ?
1/ 3
2
o Ge Be
R R A R R ? ? ? ? ? ? ?
1/3 1/ 3
2 9 72
o o
R A R A ? ? ? ? 
 
Nuclear Density  
Assuming spherical symmetry, volume of nucleus is given by 
                                 
3
4
V  R
3
? ?
3
0
4
R A
3
? ?
. 
Mass of one proton = 1.67 × 10
-27
 kg, Nuclear Mass = A × 1.67 × 10
-27
 kg. 
27
17 3
3
0
A 1.67 10
Nuclear density 10 kg / m
4
R A
3
?
? ?
? ?
? ?
  
Nuclear Particle Density = 
Nuclear Mass Density
Nuclear Mass
 
17 3
27
10 Kg/m
1.67 10 Kg/Nucleon
?
?
?
 
                                         = 10
44
 Nucleons/m
3