I need help to a extra question in an exercise in a textbook here on cramster. T

Question

I need help to a extra question in an exercise in a textbook here on cramster.
The problem is following:

The wave nature of particles results in the quantummechanical situation that a particle confined in a box can assume only wavelenghts that result in standing waves in the box, with nodes at the box walls.

A) Show that an electron confined in a one-dimensional box of length L will have energy levels given by

(Hint: Recall that the relationship between the de Broglie wavelength and the speed of a nonrelativistic particle is mv = h/. The energy of the particle is ½mv2.)

B) If a hydrogen atom is modeled as a one-dimensional box with length equal to the Bohr radius, what is the energy (in electron volts) of the lowest energy level of the electron?

The solution for A and B is on following site: http://www.cramster.com/solution/solution/295018

Explanation / Answer

E = (2n+1)h2 / 8mL2

for the transition from 1 to 2 the E = 3h2/8mL2 = 3 × (6.625 × 10 -34)2 / (8 × 9.1 × 10-31 × (5*10-10)2)

                                                                     = 7.23 × 10-19 J

E = h = hc/ = 7.23 × 10-19

so = (6.626 × 10-34 × 3 × 108 ) / ( 7.23 × 10-19) = 2.74 × 10-7 = 274.93 nm

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