Question

An electron confined in a one-dimensional box emits a

200

n
m
photon in a quantum jump from
n
=
4
to
n
=
3
. What is the length of the box?

Answer 1

The electron emits a photon with a wavelength of 200 nm in a quantum jump from n = 4 to n = 3. The length of the one-dimensional box can be calculated using the energy levels of the quantum states and the equation E(n=4) - E(n=3) = hc / lambda. The length of the box is approximately 53.9 nm.

Step-by-step explanation:

The one-dimensional box is a model used in quantum mechanics to describe the behavior of particles being confined to a region in one dimension. The energy levels of the particle in the box are given by the equation:

E = (n^2 * h^2) / (8 * m * L^2)

Where E is the energy, 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 that the electron emits a photon with a wavelength of 200 nm in a quantum jump from n = 4 to n = 3, we can use the equation to find the length of the box. Using the energy levels of the quantum states, we can equate the energy difference to the energy of the photon:

E(n=4) - E(n=3) = hc / lambda

Where c is the speed of light and lambda is the wavelength of the photon.

Substituting the equations for the energy levels and solving for L, we find that the length of the box is approximately 53.9 nm.

Answer 2

The length of the box is 300 nm.

Step-by-step explanation:

To determine the length of the box, we can use the relationship between the wavelength of the emitted photon and the width of the box. In this case, the electron emits a 200 nm photon, which corresponds to the transition from n=4 to n=3. We can use the formula:

λ = 2L/n

where λ is the wavelength, L is the width of the box, and n is the quantum number. Plugging in the values, we have:

200 nm = 2L/3

Solving for L, we find:

L = 300 nm

Therefore, the length of the box is 300 nm.