In a Rutherford scattering experiment a target nucleus has a...

In a Rutherford scattering experiment a target nucleus has a diameter of $1.4 \times 10^{-14} \mathrm{m} .$ The incoming $\alpha$ particle has a mass of $6.64 \times 10^{-27} \mathrm{kg}$ . What is the kinetic energy of an $\alpha$ particle that has a de Broglie wavelength equal to the diameter of the target nucleus? Ignore relativistic effects.

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Key Concepts

Non-Relativistic Kinetic Energy

This concept involves the calculation of kinetic energy for particles moving at speeds where relativistic effects are negligible. In this regime, the kinetic energy can be computed using the classical relation KE = p²/(2m), where p is the momentum and m is the mass of the particle. This approach facilitates the determination of kinetic energy when coupled with the de Broglie relation, especially in contexts such as scattering experiments.

de Broglie Wavelength

This concept refers to the idea that every particle exhibits wave-like behavior, characterized by a wavelength given by the relation ? = h/p, where h is Planck's constant and p is the momentum of the particle. It is fundamental in quantum mechanics, illustrating the wave-particle duality of matter, and is used to determine the momentum associated with any given matter wave.

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