__Objective__:

The objectives are** **(1) to use the emission spectrum of hydrogen atom in order to verify the relation
between energy levels and photon wavelength, and (2) to calculate Rydberg Constant**:**
**R = 1.097x10 ^{7}m^{-1}**

__Equipment__:

A computer with Internet connection, a calculator, a few sheets of paper, and a pencil

__Theory__:

When an electron in an atom receives some energy by any means, it moves to a
greater radius orbit with an energy level equal to that electron's energy**.** Such atom
is then said to be in an** ****excited
state****.** The excited state is unstable however, and the electron returns to
lower levels (orbits) by giving off its excess energy in the form of electromagnetic
radiation** **(a photon of light)**.** * Max
Planck* showed that the

E_{n} - E_{m} =
hf

where *E _{n}* is
the energy of the

Possibilities for the occurrence of * electron
jump* from one level to other
levels are numerous

*
Hydrogen* is the simplest
of
atoms

* Click* on
the following

http://www.colorado.edu/physics/2000/quantumzone/lines2.html **.**

In the above applet, if you click on a higher orbit than where the electron is
orbiting, a wave signal must be received by the electron (from outside) to give
it energy to go to that higher level**.** If the electron is already in a higher
orbit and you click on a lower orbit, then the electron loses excess energy and
gives off a wave signal before going to that lower orbit**.**

Also click on the following link**: ** http://www.walter-fendt.de/ph14e/bohrh.htm
and try both options of "Particle Mode" and "Wave Mode"**.** You can put the mouse
on the applet near or exactly on any circle and change the orbit of the electron
to anywhere you wish**;** however**,** there are only discrete orbits with circumferences
that each can accommodate an integer multiple of a certain wavelength**.** It is at those special orbits
that the applet shows * principal
quantum numbers* for the
electron on the right side of the applet

In * Fig. 1*,

The
possibilities for * electron return* are
also shown

On the other hand, some transitions are * weaker*
and result in

__Grouping of the Transitions:__

*
Transitions* made from

*
Transitions* made from

*
Transitions* made from

*
Transitions* made from

__Emission and Absorption Spectra__

** **A hot gas emits light because of the energy it receives by any means to stay
hot**.** As was mentioned earlier, the received energy by an atom sends its
electrons to higher levels, and in their returns, the electrons emit light of
different wavelengths**.** The emitted wavelengths can be observed in a
* prism
spectrometer* in the form of a few lines of different colors

** *** For white light *entering a
spectrometer

__Procedure__:

Click on** **http://mo-www.harvard.edu/Java/MiniSpectroscopy.html **.**

The "Mini Spectroscopy" Applet appears**.** At the very top it has a dropdown
window that allows you chose different hot gases**.** * First
Select the hydrogen gas. * The very top picture is what you see of hot
(excited) hydrogen if you view it through a spectrometer

* This
applet* is calibrated in

* 1)* Read the exact values of the

http://online.cctt.org/physicslab/content/PhyAPB/lessonnotes/

dualnature/discharge/index.html**.**

* 2)* Use the

* 3)* Average the

* 4)* Compare it with the

* 5)* Click on the 2nd link and observe the emission spectra for other atoms

__Data__:

__Given__: *R _{accepted} =
1.097x10^{7}m^{-1}.*

** Measured: **The hydrogen visible wavelengths are

** λ _{62} = nm, λ_{52} =
nm, λ_{42} = nm, λ_{32} = nm.**

{ λ_{62} means
the λ corresponding to transition from n = 6 to n = 2
}.

__Calculations__:

Use the * Balmer
Series* equation to
calculate

__
Comparison of the Results__:** **Calculate
a % error on **R****.**

** Conclusion:** To
be explained by students

Also,
explain why heavier elements
have more transitions visible to us**.**

** Discussion:** To
be explained by students