What is the de Broglie wavelength of an electron? What determines the value of the de Broglie wavelength for an electron?
The correct answer and explanation is:
The de Broglie wavelength of an electron is given by the equation: λ=hp\lambda = \frac{h}{p}
where:
- λ\lambda is the de Broglie wavelength,
- hh is Planck’s constant (6.626×10−346.626 \times 10^{-34} J·s),
- pp is the momentum of the electron.
The momentum pp is calculated as the product of the electron’s mass (mm) and velocity (vv): p=mvp = mv
Thus, the de Broglie wavelength is inversely proportional to the momentum of the electron. This means that as the momentum of the electron increases, its wavelength decreases.
The value of the de Broglie wavelength for an electron is determined primarily by its momentum. The momentum is dependent on two factors: the mass of the electron and its velocity. Since electrons have a very small mass (9.11×10−319.11 \times 10^{-31} kg), their momentum can vary significantly depending on their speed. If an electron moves at a higher velocity, its momentum increases, and consequently, its de Broglie wavelength becomes shorter.
In practical terms, the de Broglie wavelength of an electron becomes most noticeable in situations where the electron’s velocity is relatively low, such as in atoms or at microscopic scales. For example, in the case of an electron moving through a potential difference, the momentum and velocity are directly related to the amount of energy imparted to the electron. In these cases, the wavelength of the electron is often on the scale of atomic structures, making wave-like properties important for understanding electron behavior.
In conclusion, the de Broglie wavelength for an electron is determined by its momentum, which in turn depends on the electron’s velocity. The wavelength is inversely proportional to this momentum, meaning that faster electrons have shorter wavelengths.