Download The Behavior of Electrons in Atoms Spectrum of the Hydrogen Atom

CHEM 109
Introduction to Chemistry
Fall 2010
The Behavior of Electrons in Atoms
In this short exercise we will examine how electrons behave within an atom. We will do this by
looking at the energies of photons emitted when an excited atom relaxes. These excited atoms
can be generated by placing the atom in the very large electric field within a gas discharge tube
(think neon light) or in the heat of a Bunsen burner flame. Photons are particles of light that
carry energy.
Spectrum of the Hydrogen Atom
In the laboratory we have observed the spectrum of photons emitted by excited Hydrogen atoms.
Hydrogen is particularly important because 1H is the simplest atom possible. It contains a single
proton in the nucleus and a single electron in the remaining space of the atom.
This atom produced three spectral lines; Red, Blue, and Violet. These lines are only a part of the
complete spectrum of Hydrogen. Other spectral lines occur in the Ultraviolet and Infrared
regions of the electromagnetic spectrum. However, our eyes are not capable of registering these
photons and so we do not see them. A more complete spectrum for Hydrogen is attached. We
now wish to convert the energies of the emitted spectral photons into atomic energy levels for the
excited atom.
We do this by recognizing that photons are emitted when the atom transitions from a high energy
state (excited) to a low energy state. This can be represented diagrammatically as below:
Questions:
1.
What is the minimum number of quantum states required to explain the three spectral lines
observed in the laboratory? Diagram these and identify the transitions responsible for
producing each spectral line. Your diagram should be to scale. (You calculated the needed
photon energies in the last laboratory exercise.) What assumption do you have to make in
order to construct this diagram?
2.
Our visible spectral lines are part of a grouping of spectral lines called the Balmer Lines.
What do you notice is happening to the lines in this series as the energy of the emitted
photons increases? What implications does this have for the energies of Hydrogen’s
quantum states? Indicate this on your energy diagram?
3.
What additional piece of information do you need in order to confirm the order of your
quantum states is correct? (Hint: Look to the complete Hydrogen spectrum for the spectral
line that will provide the needed information.) Consult your Teaching Assistant for the
information you need.
4.
What are the photon energies associated with the first two spectral lines of the Lyman
Series that occurs in the Ultraviolet region of the electromagnetic spectrum? How will
your energy diagram need to be modified in order to account for the quantum states
associated with these spectral lines? Re-draw your energy diagram to account for the new
quantum states. The lowest energy state possible is referred to as the Ground State. Label
this in your diagram. Each quantum state is labeled with a quantum number; starting with
the ground state (n=1). The other states are labeled consecutively with integer increases.
Label each state in your diagram with its quantum number. What is the largest quantum
number possible?
Interactions within the Hydrogen Atom
5.
What is the nature of the interaction between Hydrogen’s nucleus and its electron?
6.
Will this interaction be stronger or weaker as the electron moves away from the nucleus?
7.
Bohr built one of the first successful models of the Hydrogen atom. In this model, the
electron orbits the nucleus with a given velocity.
Which are energetically more favorable, orbits close to the nucleus or those further from
the nucleus? Explain your choice.
8.
Why will the electron’s velocity not cause it to fly out of the atom?
9.
What is the minimum number of orbits required to account for the three visible spectral
lines of the Balmer series? Correlate each orbit with a quantum state in your energy
diagram by labeling the orbits with an appropriate quantum number.
10.
By balancing the Centrifugal and Electrical forces within the atom, Bohr was able to
develop an expression for the radius of the electron’s orbit based on the orbit’s quantum
number (n).
radius = 0.052917 x n2
Sketch to scale the orbits associated with the first 4 quantum states.
11.
What “orbit” is associated with the “largest” quantum number?
Hydrogen-Like Atoms
The following atoms are called Hydrogen-like atoms:
He+, Li2+, Be3+, etc.
12.
How are these atoms Hydrogen-like? What is the next atom in this series?
13.
How will the orbits of the electrons in these atoms differ from the corresponding orbits in
the Hydrogen atom? Explain your reasoning.
14.
Bohr’s model for the Hydrogen atom can be modified to include these Hydrogen-like
atoms by including the charge on the nucleus (Z):
radius = 0.052917 x Z x n2
Sketch to scale the orbits associated with the first 4 quantum states for He+.
14.
What will happen to the spectral lines associated with these states when compared to
similar states in the Hydrogen atom? Explain your reasoning.
Helium Atom
Now consider the next more complex atom; that of 4He.
15.
What additional interactions occur within this atoms?
Appendix - Complete Emission Spectrum of Hydrogen