A Level Physics Practice Exam

What is the relationship used to calculate the de Broglie wavelength?

1. Wavelength equals mass times velocity

2. Wavelength equals Planck's constant divided by momentum

3. Wavelength equals energy divided by frequency

4. Wavelength equals velocity divided by frequency

The correct answer is: Wavelength equals Planck's constant divided by momentum

The correct relationship for calculating the de Broglie wavelength is expressed as the wavelength being equal to Planck's constant divided by momentum. The de Broglie hypothesis states that any moving particle or object has an associated wavelength, which can be derived from its momentum. Mathematically, this is represented as: \[ \lambda = \frac{h}{p} \] where \( \lambda \) is the wavelength, \( h \) is Planck's constant, and \( p \) is the momentum of the particle (which is the product of mass and velocity). This relationship is fundamental in quantum mechanics and highlights the wave-particle duality of matter, showing that particles such as electrons behave like waves under certain conditions. The concept helps explain phenomena such as electron diffraction and the behavior of particles at the quantum level, reinforcing the idea that wavelength is inversely related to momentum. Other options presented do not accurately represent the de Broglie wavelength. For example, one option incorrectly suggests a direct multiplication of mass and velocity to yield wavelength, which does not align with the established quantum mechanics. Another option involves energy and frequency, which relates to wavelength in a different context, principally with electromagnetic radiation rather than matter. Finally, the relationship involving