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suppose an attractive nuclear force acts between two protons which may be written as f=ce**(-kr)/r**2.

suppose an attractive nuclear force acts between two protons which may be written as f=ce**(-kr)/r**2. 

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Arun
25750 Points
5 years ago
F = C · exp{-k · r} / r² 

The argument of the the exponential function must be dimensionless. Because r has the dimension length (SI-Unit m) k must have the reciprocal of this dimension: 
k · r [=] 1 
→ 
k · m [=] 1 
→ 
k [=] m^-1 

The force Force has the SI Unit Newtons defined as 
1N = 1kg·m/s² as dimension. 
Hence: 
C · exp{-k · r} / r² [=] F 
→ 
C · 1 / m² [=] N 
→ 
C = N · m² = kg·m³/s² 

(b) 
The repulsive electrostatic force is given by Coulombs law: 
F = kc · |q₁| · |q₂| / r² 
kc is the electrostatic constant kc = 8.988×10^9 N·m²/C² 
q are the charges here both the proton charge 
|q₁| = |q₂| = 1.6022×10^-19 C 

Both Forces are equal: 
kc · |q|² / r² = C · exp{-k · r} / r² 
→ 
C = kc · |q|² / exp{-k · r} 
= kc · |q|² · exp{k · r} 
= (8.988×10^9 N·m²/C²) · (1.6022×10^-19 C)² · exp{1 fermi^-1 · 5 fermi} 
= 3.424 ×10^-2

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