Question

In an experiment to measure the effect of the de Broglie wavelength of an electron passing over a barrier, the value of t = 1 occurs when an integral or half-integral number of de Broglie wavelengths equal the width l of the barrier. You are planning this experiment and need to estimate the electron energies e that will result in t = 1. Assuming a barrier height of e = 12 ev and a width of 1.7 × 10⁻¹⁰ m, what is the estimated electron energy?

Answer 1

To estimate the electron energy resulting in t = 1, we can use the de Broglie wavelength equation and the relation between energy and momentum.

Step-by-step explanation:

To estimate the electron energy that will result in t = 1, we can use the de Broglie wavelength equation:

λ = h / p

where λ is the de Broglie wavelength, h is the Planck constant, and p is the momentum of the electron.

We can rearrange the equation to solve for the momentum:

p = h / λ

Given that the integral or half-integral number of de Broglie wavelengths equal the width l of the barrier when t = 1, we can substitute l for λ in the equation:

p = h / l

Now, we can solve for the energy E using the relation:

E = p^2 / (2m)

where m is the mass of the electron. Plugging in the values for h, l, and m, we can calculate the estimated electron energy.