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Rutherford Scattering Formula:
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Rutherford scattering refers to the elastic scattering of charged particles by the Coulomb interaction. It is named after Ernest Rutherford, who used this phenomenon to discover the atomic nucleus in his famous gold foil experiment.
The calculator uses the Rutherford scattering formula:
Where:
Explanation: The formula shows that the number of particles scattered at a given angle is inversely proportional to the fourth power of the sine of half the scattering angle.
Details: Rutherford scattering was crucial in establishing the nuclear model of the atom. It demonstrated that atoms have a small, dense, positively charged nucleus surrounded by electrons, revolutionizing our understanding of atomic structure.
Tips: Enter the Rutherford scattering constant and scattering angle in radians. Both values must be positive numbers. The scattering angle should be between 0 and π radians for meaningful results.
Q1: What is the physical significance of the Rutherford scattering constant?
A: The constant κ depends on factors like the atomic number of the target nucleus, the energy of the incident particles, and the number of incident particles.
Q2: Why does the formula use sin(θ/2) to the fourth power?
A: This mathematical form arises from the inverse square law of the Coulomb force and the geometry of the scattering process in the Rutherford model.
Q3: What was the significance of Rutherford's gold foil experiment?
A: It provided the first experimental evidence for the nuclear model of the atom, showing that most of the atom's mass and positive charge is concentrated in a tiny nucleus.
Q4: Are there limitations to the Rutherford scattering formula?
A: Yes, it assumes point charges and doesn't account for quantum mechanical effects, nuclear size, or relativistic corrections that become important at high energies.
Q5: How is this formula used in modern physics?
A: Rutherford scattering principles are still used in various fields including materials science, nuclear physics, and particle physics for studying atomic and nuclear structures.