**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*E) =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 *eV*