Wavelength of an Alpha Particle. An alpha particle (m=6.64 ×10^-27 kg) emitted in the radioactiv

step 1 Okay, in this problem we have an alpha particle being emitted in a nuclear decay of uranium. Thi

Wavelength of an Alpha Particle. An alpha particle (m=6.64...

Wavelength of an Alpha Particle. An alpha particle $\left(m=6.64 \times 10^{-27} \mathrm{kg}\right)$ emitted in the radioactive decay of uranium-238 has an energy of 4.20 $\mathrm{MeV} .$ What is its de Broglie wavelength?

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Key Concepts

Planck's Constant

Planck's constant (h) is a fundamental constant in quantum mechanics that relates the energy of a photon to its frequency. In de Broglie's equation, it serves as the proportionality constant linking a particle's momentum to its wavelength, underscoring the quantum nature of matter.

Energy Unit Conversion

In problems where energy is provided in units such as electronvolts (eV or MeV), converting these units to joules is crucial for consistency in the International System of Units (SI). This step ensures that all constants and computed quantities, such as momentum and wavelength, are compatible.

de Broglie Hypothesis

This fundamental quantum concept posits that every moving particle has an associated wavelength, given by the equation ? = h/p, where h is Planck’s constant and p is the particle's momentum. It bridges the gap between classical and quantum physics by introducing wave-particle duality.

Momentum and Kinetic Energy Relationship

For nonrelativistic particles, the momentum can be derived from kinetic energy using the relation p = ?(2mE), where m is the mass and E is the kinetic energy. This relation is essential for converting energy information into momentum, which is then used to determine the de Broglie wavelength.

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