1.

Suppose the magnitude of nuclear forces between two protons varies with the distance between them as shown in figure (4-Q1). Estimate the ratio "Nuclear force/Coulomb force" for (a) x=8 fm (b) x=4 fm, (c) x=2 fm and (d) x=1 fm (1 fm =10-15 m).

Answer»

In the given figure force on the Y-axis is plotted on a logarithmic scale. Magnitude of Nuclear forces from the given figure by logarithmic interpolations are, 

For x=8 fm, => 0.18 N   

For x=4 fm, => 1.00 N    

For x=2 fm, => 17.7  N  

For x=1 fm, => 177 N  

Now Coulomb force is given by, F=q²/4π ε0 r²  = 9x109 .e²/r² = 9x109 .(1.6x10-19 )²/r². (10-15)2   = 144/r² N (Here r is in fm)   

So this force, 

for x=8 fm, => 2.25 N  

for x=4 fm, => 9.00 N  

for x=2 fm, => 36.00 N  

for x=1 fm, => 144.0 N    

So the ratio "Nuclear force/Coulomb force"    

(a) for x=8 fm is  0.18 N/2.25 N = 0.08  

(b) for x=4 fm is  1.0 N/9.0 N = 0.11   

(c) for x=2 fm is  17.7 N/36.0 N = 0.491  

(d) for x=1 fm is  177 N/144 N = 1.23   

It is clear that in the range of r< 2 fm Nuclear forces are quite comparable to Coulomb forces.



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