Download CH 115 Fall 2014Worksheet 2 Express the following values in

CH 115 Fall 2014
Worksheet 2
1. Express the following values in scientific notation.
a). 61,500
6.15 x 104
b). 0.0000568
5.68 x 10-5
c). 64,960,000
6.496 x 107
d). 0.07058 7.058 x 10-2
2. A sample of naturally occurring silicon consists Si-28 (amu = 27.9769), Si-29 (amu =
28.9765) and Si-30 (amu = 29.9738). If the atomic weight of silicon is 28.0855 and
the natural abundance of Si-29 is 4.67%, what are the natural abundances of Si-28
and Si-30?
This is an example of a REVERSE atomic weight calculation!
AW = (amu)x(% abundance) of each isotope
28.0855 = (27.9769)(x) + (28.9765)(.0467) + (29.9738)(y)  I substituted x
and y for the missing percentages first.
We also know that x + y + .0467 = 1. All the percentages must add up to 100
always. We can solve this equation for y  y = .9533 – x  We can substitute
this expression for y in our equation. The whole purpose of this is to have ONE
EQUATION WITH ONE VARIABLE.
28.0855 = (27.9769)(x) + (28.9765)(.0467) + (29.9738)(.9533 – x)
Now we can solve for x using all our known rules in algebra.
28.0855 = 27.9769x + 1.35320255 + 28.57402354 – 29.9738x (Distribute)
28.0855 = -1.9969x + 29.92722609 (Combine like terms)
-1.84172609 = -1.9969x (Get x by itself)
.9223 = x (Divide to isolate x)
x represents the percentage of Si-28 present in the sample. Now you can plug
back in and solve for y (percentage of Si-30) since all your percentages have to
add up to 100.
y = 1 - .9223 - .0467 = .031
Natural abundance of Si-28 is 92.23% and of Si-30 is 3.1%.
3. If it takes 3.36 x 10-19 J of energy to eject an electron from the surface of a certain
metal, calculate the longest possible wavelength, in nanometers, of light that can
ionize the metal.
Working backwards from energy, we should start with the equation E = hv,
and solve for the frequency.
CH 115 Fall 2014
Worksheet 2
E = hv  v = E / h (plug and chug) = 3.36 x 10-19 J / 6.626 x 10-34 Js =
5.070932689 x 1014 1/s (DO NOT ROUND YET, ONLY AT THE END OF A
PROBLEM)
Now that we have frequency, we can use the equation c = wavelength x
frequency to get the wavelength.
Wavelength = c / frequency = 2.99 x 108 m/s / 5.070932689 x 1014 1/s =
5.89635119 x 10-7 m
The question asks for the wavelength in nanometers, so we have to covert our
answer from meters to nanometers.
5.89635119 x 10-7 m x 109 nm = 589.64 nm (feel free to round now!)
4. Describe the observed line spectra graph. Include observations about emitting and
absorbing energy and relative energy level transitions.
This is the simplest version I could find – there’s probably a better one in your
book so check it out!
A line spectra graph or a Bohr diagram describes energy levels of the electrons
present in the atom. Energy level is represented by the n on the right side of the
diagram and as we increase n, we increase in energy. If an electron moves up the
diagram (say from 1 to 2) it is ABSORBING energy. If it moves down the diagram
(from 2 to 1) it is EMITTING or RELEASING energy. Notice that the gaps between
energy levels are larger at the bottom and smaller at the top. It becomes easier
(takes less energy) to shift energy levels at the top than at the bottom. In other
words, it takes a whole lot of energy to move from n=1 to 2, while it takes only a
little energy to move from n=3 to 4.
CH 115 Fall 2014
Worksheet 2
5. What are the four quantum numbers used to describe an electron and what about
the electron do they describe?
Quantum numbers are used to describe aspects of an electron present in a
particular atom. The term “quantum” comes from the word quantized, which
means a discrete unit or packet. So basically electrons are present in discrete
units and are only allowed to be present in these specific locations/energy
levels. There are four quantum numbers used in general chemistry to describe
characteristics of an electron.
Principal quantum number (abbreviated n) – determines size and RELATIVE
ENERGY (what energy level the electron is in
- Can be any positive integer (from 1 to infinity)
- Also corresponds to the row of the element in the periodic table, ex.
An electron in the lithium atom has a principal quantum number of
n=3
- As you increase the number, the energy increases
Subsidiary quantum number (abbreviated l) – determines shape or the
subshell the electron is present in (each subshell has a characteristic shape)
- Can be any number from 0 to (n-1)  for an electron with n = 3, l can
be 0, 1, or 2
- Each subshell can also be represented by a letter (0 = s, 1 = p, 2 = d, 3
= f)  corresponds to blocks on the periodic table
- Shapes: s = sphere, p = dumbbell, d = dumbbell inside a doughnut
hole, etc. (look in your book if you don’t understand this)
Magnetic quantum number (abbreviated ml) – determines the orientation of
the subshell that the electron is in or the orbital (each subshell will have a
particular number of orbitals)
- Can be any number from –l to +l  for an electron with l = 1, ml can
be -1, 0, or 1 (this subshell has THREE possible orientations)
- Generally, s has 1 orientation, p has 3, d has 5, and f has 7
Spin quantum number (abbreviated ms) – determines which direction the
electron is spinning
- Only two possible spins (-1/2 or +1/2)
- There are two electrons in every orientation or orbital  each of
these electrons has a different spin (one is + and one is – ALWAYS)