Question

If an electron is accelerated through a potential difference, how does the de Broglie wavelength of that electron change as its kinetic energy increases?

Accepted Answer

As an electron is accelerated through a potential difference—the electrical energy used to push a charged particle—it gains kinetic energy, which is the energy an object possesses due to its motion. According to the de Broglie hypothesis, all moving particles exhibit wave-like properties characterized by a de Broglie wavelength, which is inversely proportional to the particle&#x27;s momentum. Because the kinetic energy of the electron increases as it accelerates, its speed and momentum must also increase. Since a shorter wavelength corresponds to a higher momentum, the de Broglie wavelength of the electron decreases as its kinetic energy increases. You can visualize this relationship like a musical string: just as tightening a string increases its tension and makes the vibrating wave shorter and higher-pitched, increasing an electron&#x27;s energy effectively &#x27;tightens&#x27; its wave, resulting in a shorter wavelength.

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If an electron is accelerated through a potential difference, how does the de Broglie wavelength of that electron change as its kinetic energy increases?

As an electron is accelerated through a potential difference—the electrical energy used to push a charged particle—it gains kinetic energy, which is the energy an object possesses due to its motion. According to the de Broglie hypothesis, all moving particles exhibit wave-li....