In a Rutherford scattering experiment, the kinetic energy of the incident α-particles is increased from K to 3K. The target foil, detector solid angle and scattering angle remain unchanged. If the new count rate is 1 ÷ N times the original count rate, find N.
Physics · Atomic Structure and X-rays · atomic structure and bohr atomic model
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Question

In a Rutherford scattering experiment, the kinetic energy of the incident α-particles is increased from K to 3K. The target foil, detector solid angle and scattering angle remain unchanged. If the new count rate is 1 ÷ N times the original count rate, find N.

Physics · Atomic Structure and X-rays · atomic structure and bohr atomic model

G1 Physics · Accepted Answer

For fixed target and angle, the Rutherford scattering count varies inversely as the square of incident kinetic energy: N(scattered) ∝ 1 ÷ K². When the kinetic energy becomes 3K: new count ÷ old count = K² ÷ (3K)² = 1 ÷ 9. Thus the new count is 1 ÷ 9 of the original count. Hence N = 9.