A photon with wavelength is absorbed by an electron confined to a box. As a resu

Question

A photon with wavelength is absorbed by an electron confined to a box. As a result, the electron moves from state n 1 to n 3. Use the following as necessary: h, m, c, and n.) (a) Find the length of the box. (b) What is the wavelength n' of the photon emitted in the transition of that electron from the state n 3 to the state n 2? Need Help? Read It -3 points SerPSE9 41. P.043.WI A particle of mass 2.05 x 10 28 kg is confined to a one-dimensional box of length 1.97 x 10 10 m. (a) For n 1, what is the particle's wavelength? (b) For n 1, what is its momentum? kg m/s (c) For n 1, what is its ground-state energy? eV

Explanation / Answer

The energies of the confined electron are

En= (h2 * n2) / 8 me * L2

Its energy gain in the

quantum jump from state 1 to state 3 is

(h2 * (32- 12)) / 8 me * L2

and this is the photon energy: (h2 * 8) / 8 me * L2 = h * f = h*c /

L = [ (h* ) / me*c]1/2

b) Let ' represent the wavelength of the photon emitted:

h*c/' = h2 *32/ 8*me*L2 - h2 *22/ 8*me*L2 = 5 *h2/ 8*me*L2

(h*c/) * ('/h*c) = 1/5 ( from above equations)

' = 0.2

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.