An electron with kinetic energy 5.0 eV traveling in a region in which the potential energy is zero is incident at x 0 on a potential barrier of height 3.0 eV.What is the wavelength of the electron in the region x 0?

Question

An electron with kinetic energy 5.0 eV traveling in a region in which the potential energy is zero is incident at x > 0 on a potential barrier of height 3.0 eV.What is the wavelength of the electron in the region x > 0?

Quizplus · Accepted Answer

The wavelength of the electron in the region x > 0 can be calculated using the de Broglie wavelength formula, $\lambda = \frac{h}{p}$, where $h$ is Planck's constant and $p$ is the momentum of the electron. The kinetic energy (KE) of the electron is given as 5.0 eV, and since the potential energy in the region is zero, the total energy is equal to the kinetic energy. The momentum $p$ can be found from the kinetic energy using the relation $KE = \frac{p^2}{2m}$, where $m$ is the mass of the electron. Solving for $p$ gives $p = \sqrt{2mKE}$. Substituting the values (with $KE$ converted to Joules) and using $h = 6.626 \times 10^{-34} m^2 kg / s$ and $m = 9.109 \times 10^{-31} kg$, we find the wavelength $\lambda$. The correct calculation leads to a wavelength close to 0.87 nm, making option A the correct choice.

An Electron with Kinetic Energy 5