Conceptual Questions:
1. Explain why the exclusion principle leads to the periodic table of the elements.
2. Show that confining an electron to a position within a nucleus (size about 10-14 m) gives it an impossibly large momentum.
3. The quantum mechanical model of the hydrogen atom suggests a visual picture of the electron as which of the following?
a. raisin in pudding
b. probability cloud
c. planetary orbiting body
d. light quantum
4. In an analysis relating Bohr's theory to the de Broglie wavelength of electrons, when an electron moves from the n = 1 level to the n = 2 level, the circumference for its orbit becomes 4 times greater. This occurs because:
a. there are four times as many wavelengths in the new orbit.
b. the wavelength of the electron becomes four times as long.
c. there are twice as many wavelengths and each wavelength is
twice as long.
d. the electron is moving four times as fast.
Numerical Problems: help is at the end of the page.
1. How many electrons are in aluminum's (atomic number 13) outer shell?
ans: 3
2. What is the wavelength of the line in the Balmer series of hydrogen that is comprised of transitions from the n = 4 to the n = 2 level?
ans: 486 nm
3. If the radius of the electron orbit in the n = 1 level of the hydrogen atoms is 0.053 nm, what is its radius for the n = 4 level? (Assume the Bohr model is valid.)
ans: 0.85 nm
4. The quantum mechanical model the atom requires that if the orbital quantum number = 4, there are permitted how many possible substates?
ans: 18
Help
1. Each principle shell contains 2*n*n states.
2. 1/l = R*(1/4 - 1/n*n)
3. r = n*n*ao
4. 2(2l+1)