InterviewSolution
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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). |
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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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