Question

In an experiment, a beam of electrons of energy E = 4eV is incident on a barrier of height V0 = 3 eV and width a = 1 nm (nm =nanometer). What fraction of the incident beam will be reflected by this potential barrier?

Answer 1

To determine the fraction of the incident beam that will be reflected by the potential barrier, we can use the concept of quantum tunneling. This probability depends on factors such as the energy of the particle and the height and width of the barrier. For an electron with energy E = 4 eV incident on a barrier with height V0 = 3 eV and width a = 1 nm, the transmission probability can be calculated using the formula T = e^(-2ka).

Step-by-step explanation:

To determine the fraction of the incident beam that will be reflected by the potential barrier, we can use the concept of quantum tunneling. When a particle encounters a potential barrier, there is a probability that it can penetrate the barrier and continue on the other side.

This probability depends on factors such as the energy of the particle and the height and width of the barrier.

1. For an electron with energy E = 4 eV, incident on a barrier with height V0 = 3 eV and width a = 1 nm, we can calculate the transmission probability using the formula:
2. T = e^(-2ka)
3. In this formula, k is the wave number given by:
4. k = sqrt(2m(E - V0)/ħ)
5. Where m is the mass of the electron and ħ is the reduced Planck's constant. Plugging in the values:
6. m = 9.11 x 10^-31 kg
7. ħ = 1.05 x 10^-34 J·s
8. We can calculate the value of k and then use it to calculate the transmission probability.