**Examples for quantum physics**

Example #1

Problem:

a.) What is the energy of a single photon
(in *eV*) from a light source with a wavelength of 400 *nm*?

Solution:

Use * E* =

3.1 *eV*

b.) If a 50 *W* laser emits 400 *nm*
light, how many photons are emitted in 10 seconds?

Solution:

In 10 seconds, 500 Joules=500/1.6E-19 *eV* of
photons are emitted. Dividing this total energy by the energy per photon gives the total
number of photons.

1.01E21

Example #2

Problem:

a.) Suppose light of wavelength 400 *nm*
is incident on a metal with a work function * W* = 5.5

Solution:

From the previous problem, the energy of a single 400 *nm*
photon is 3.1 *eV*. One must therefore reduce the effective work function to 3.1 *eV*
to allow the light to liberate an electron.

2.4 *eV*

Example #3

Problem:

a.) A completely ionized Carbon nucleus is
accelerated through a potential difference of 7000 volts. What is the final kinetic energy
of the carbon? DATA: The charge of carbon is 6*e* and the mass is 12 proton masses.

Solution:

Use * KE* =

* KE*
= 42.0

b.) What is the DeBroglie wavelength of the Carbon?

Solution:

Use **p** = **h****/****l . **But first
one must use

* p* = sqrt(2*m*KE) =1.64E-20

**l** = 4.04E-14 *m*

Example #4

Problem:

a.) A monoenergetic beam of marbles which
have a mass of 5.0 *g* is hurled into a board with two slits. The velocity of the
marbles is 15.0 *m/sec*, and the slits are separated by 6.0 *cm. *How far
from the slits must one place a screen to get an interference pattern where the first
interference maxium is 20 *cm* from the central peak?

Solution:

First find the wavelength using * p*
=

* L*
= 1.36E30

Example #5

Problem:

a.) An electron is confined to a box of
length 0.6 *nm* (a typical atomic size). From the uncertainty principle, estimate
the minimum kinetic energy (in *eV*) of the electron.

Solution:

The momentum must be of order * h/L*.
One can then estimate the kinetic energy with

* KE = *8.4

Example #6

Problem:

a.) Which stars are hotter, blue stars or red stars?

Blue, because blue light has a shorter wavelength, and more energetic photons.

b.) Assuming that the Earth
has a mean temperature of 300 degrees Kelvin and is located a distance of 1.5E10 *m*
from the sun*, *estimate the power output of the sun.

Solution:

The power emitted from the Earth by radiation is
*4**p**R _{e}^{2}*

**P** =
5.2E26 Watts