An electron confined in a one-dimensional box emits a 200 nm photon in a quantum jump from n=2 to n =1. What is the length of the box?
Tthe length of the box is
An electron confined in a one-dimensional box emits a 200 nm photon in a quantum jump from n=2 to n =1.
Energy levels of the particle in the box:
Energy of the photon:
Substitute energy levels:
Substitute energy of the photon:
Express the above equation in terms of L:
Substitute the values:
The first three energy levels of the fictitious element X were shown in FIGURE P38.56. An electron with a speed of 1.4 X 106 m/s collides with an atom of element X. Shortly afterward, the atom emits a photon with a wavelength of 1240 nm. What was the electron's speed after the collision? Assume that, because the atom is much more massive than the electron, the recoil of the atom is negligible. Hint: The energy of the photon is not the energy transferred to the atom in the collision.
FIGURE Q38.9 is a simulation of the electrons detected behind two closely spaced slits. Each bright dot represents one electron. How will this pattern change if
a. The electron-beam intensity is increased?
b. The electron speed is reduced?
c. The electrons are replaced by neutrons?
d. The left slit is closed?
Your answers should consider the number of dots on the screen and the spacing, width, and positions of the fringes.
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