An electron in a 10.0-nm one-dimensional box is excited from the ground state into a higher energy state by absorbing a photon with wavelength 1.374 × 10^-5 m. Determine the final energy level for this transition. A) n = 6 B) n = 4 C) n = 2 D) n = 5 E) n = 3

Question

Quizplus · Accepted Answer

The energy of a photon can be calculated using the equation:
E = hc/λ
where h is Planck's constant, c is the speed of light, and λ is the wavelength of the photon.

We can rearrange this equation to calculate the final energy level of the electron:
E = hc/λ = (6.626 × 10^-34 J s) × (3.00 × 10^8 m/s) / (1.374 × 10^-5 m) = 1.45 × 10^-17 J

The energy level of a particle in a 1D box is given by the equation:
En = n^2h^2/8mL^2
where n is the principal quantum number (the energy level), m is the mass of the particle, and L is the length of the box.

We can rearrange this equation to solve for n:
n = sqrt(8mL^2En)/h

Plugging in the given values and solving for n, we get:
n = sqrt(8(9.11 × 10^-31 kg)(10.0 × 10^-9 m)^2(1.45 × 10^-17 J) / (6.626 × 10^-34 J s)^2) = 5.13
Rounding to the nearest integer gives us n = 5.

Therefore, the final energy level for this transition is n = 5. Answer: D).

An Electron in a 10