Question

Consider a particle trapped in a box that can be viewed as an infinite square well. The energy levels of such a particle are given by

En = n²h² / 8mL² , n = 1,2,3,…
Take the mass of the particle to be 1.67×10² kg and the box size L to be 10 nm.
(a) Compute the first four energy levels.

Answer 1

The energy levels of a particle trapped in an infinite square well can be calculated using the formula En = n²h² / 8mL². By plugging in the given values, the first four energy levels can be computed.

Step-by-step explanation:

The energy levels of a particle trapped in an infinite square well, also known as a particle trapped in a box, can be calculated using the formula En = n²h² / 8mL², where n is the quantum number, h is Planck's constant, m is the mass of the particle, and L is the length of the box.

Given the mass of the particle as 1.67×10² kg and the box size as 10 nm, we can plug these values into the formula to calculate the energy levels.

For n = 1, the energy level is E₁ = (1² * h²) / (8 * 1.67×10² * (10×10⁻⁹)²)

Similarly, for n = 2, the energy level is E₂ = (2² * h²) / (8 * 1.67×10² * (10×10⁻⁹)²)

For n = 3, the energy level is E₃ = (3² * h²) / (8 * 1.67×10² * (10×10⁻⁹)²)

And for n = 4, the energy level is E₄ = (4² * h²) / (8 * 1.67×10² * (10×10⁻⁹)²)