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Question

With what velocity should an alpha- particle travel toward the nucleus of a copper atom at a distance of 10-13m from the nucleus of the copper atom ?


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Solution

Step 1: Given data:

  1. We know that mass (m) of α-particle is 4×massofproton=4×1.6×10-27
  2. Also, with velocity u and Z as atomic number, e as electron charge and the required values are,
    Z(Atomic number of copper)=29e=1.6×10-19ε0=8.85×10-12r=10-13

Step 2: Calculate velocity of Alpha-particle:

The kinetic energy of alpha particle will be equal to potential energy, so
12mu2=14πϵ×2ze2ru2=4ze24πϵ.m.r=29×1.6×10-1923.14×8.85×10-12×4×1.672×10-27×10-136.3×106m/sec

Hence, the velocity of an alpha particle is 6.3×106m/sec.


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