unit 1 conceptual questions
The fourth quantum number, ms , can have the value of
+½ or -½
Differentiate between the terms "subshell" and "orbital."
A subshell refers to the type of orbital: s, p, d or f and can be determined from the quantum number l. Within a subshell there can be one (s), three (p), five (d) or seven (f) orbitals. The quantum number ml tells us in which exact orbital an electron is residing
Classical mechanics made a prediction about the frequencies of light emitted by black body radiators at higher and higher temperatures. What was this prediction and did it match the experimental observations?
According to classical theory, higher and higher temperatures, radiators would emit light of ever-increasing energy. The math behind the classical theories predicted that radiators would produce extremely high-energy radiation at significant temperatures. However, experimental data proved these predictions false.
What is Bohr's model of the atom?
Bohr's model depicts an atom with a central nucleus surrounded by fixed energy levels (or shells). Electrons reside on these fixed energy levels.
How did the Bohr's model and Rydberg's equation each explain line spectra?
Bohr's model showed that there are discrete energy levels between which electrons can move. This would explain the sharp absorption and emission lines seen in the spectra. Rydberg's equation showed how to calculate these energy gaps between different levels. He determined the wavelengths of light that correspond to the lines observed in a spectrum. He then gave each energy level (n) a whole number value starting at 1 and discovered that a move by an electron between whole number energy levels could correspond to the lines observed in the spectra.
Within multi-electron atoms, the fact that the 2s orbital is lower in energy than the 2p orbitals is called a
loss of degeneracy within energy levels."
This scientist's suggestion indicated that the emission of a particular frequency requires an oscillator to have a ... energy. Since physical objects have a limited number of oscillation energies, they have a limited number of emitted frequencies.
minimum/ specific
Describe the figure and explain how frequency and work function (Φ) relate to the kinetic energy of the emitted electron.
1 photon from the light source corresponds to 1electron ejected if and only if the energy of the photon, hνis greater than the work function of the metal, Φ. Nothing happens if hν<Φ. Even if you make the light source really bright by increasing the intensity and therefore have more photons hitting the metal, no electrons will be ejected as long as hν<Φ. If hν> Φ, the kinetic energy of the ejected electron increases as the energy difference between hνand Φ increases.
Rank the following five electron transitions in the hydrogen atom from longest to shortest wavelength (think of the Rydberg equation)
14→6 > 7→3 > 4→2 > 5→2 > 3→1
Rank the following five electron transitions in the hydrogen atom from highest energy to lowest energy (think of the Rydberg equation) 2→1 4→2 4→3 5→2 5→1
5→1 > 2→1 > 5→2 > 4→2 > 4→3
Recalling that photon of 5.1 electron volts (eV) of energy will eject an electron from a piece of gold, what would happen if you were to shine a light of 6.5 eV on the gold surface? How is this the same or different from using light of 3.0 eV? What if the metal was Cesium (Φ = 2.1 eV) or Platinum (Φ = 6.35 eV) instead?
6.5 eV is greater than the work function of gold (5.1 eV), so the electron would be ejected from the gold surface. The electrons that are ejected would be faster than electrons ejected while using 5.1 eV light. Light of 3.0 eV cannot overcome the work function for gold, so no electron would be ejected. For Cs, both 6.5 eV and 3.0 eV would eject an electron because the work function is so low. Again, electrons would be faster when the 6.5 eV light is used compared to the 3.0 eV light. For platinum only the 6.5 eV light will be enough to eject an electron. When the 6.5 eV light is being used, the electrons from Cs will be fastest, the electrons from Au will have intermediate speeds and the electrons from Pt will be the slowest.
What are the two components that make up electromagnetic radiation?
Electromagnetic radiation is the result of an oscillating magnetic field perpendicular to an oscillating electric field.
What does the phrase wave-particle duality mean in your own words?
Light has both wavelike and particle like behaviors. We use the term "wave-particle duality" to describe this dual nature of light
The scientist ... suggested a solution to this problem dubbed the Ultraviolet Catastrophe.
Max Planck
Orbitals hold up to two electrons and because of the ... principle a fourth quantum number is needed.
Pauli Exclusion
What is Rydberg's equation?
Rydberg plotted, , "wavenumber" (the number of waves that can fit a "unit length" of 1) versus the difference of squared integer values (n). The equation relates the amount of energy absorbed or released (∆E) when an electron moves from one energy level (ni) to a different one (nf). The slope of both linear relationships is R, the Rydberg constant.
How are the energy solutions to the Schrödinger equation related to Rydberg's solutions and Bohr's model?
The Schrödinger equation provides exact energy solutions for the energy levels of an atom. Rydberg's calculations provide the energy differences that correspond to the differences in the quantum mechanical energy values. Bohr's model continues to illustrate these discrete differences in energy levels for an atom.
quantum number l
The angular momentum. It indicates the subshell, or type or orbital; 0 < l < n-1
Describe the relationship between frequency of incident light and the kinetic energy of ejected electrons.
The kinetic energy of a sodium electron increases linearly with increasing frequency of incident light. However, the frequency of incident light must be above a certain threshold frequency Φ in order for the electron to be ejected. This is the "work function" of a metal. Each metal has a different work function based on its own particular properties.
Would you expect the line of spectra of different elements to be the same or different? Why?
The line spectra of different elements should be distinctly different. Each element has unique energy levels. Electrons move between these distinct levels when they absorb or emit energy
quantum number ml
The magnetic quantum number indicates a particular orbital, not just a type; -l < ml < +l
quantum number n
The principle quantum number. It indicates the energy level; n greater than zero
. Briefly explain Heisenberg's uncertainty principle in your own word
The uncertainty principle tells us that the location of an object and its trajectory/path/velocity/momentum cannot both be known at the same moment in time
Explain your answer choice in question 2 above. Devise experiments that would produce the other three outcomes that you did not choose.
Using higher energy light (lower wavelength) means that more energy is transferred to the electrons as kinetic energy. In order to produce answer choice "a" as a result, we would need to maintain a 500 nm light source but lower the intensity. The energy of the light dictates the kinetic energy of the electrons. Intensity affects the number of electrons emitted. In order to produce answer choice "b" as a result, we would need to increase the wavelength of light until the frequency of light is below the necessary work function of the metal being used. In order to produce answer choice "d" as a result, we would have to maintain the same setup and not change the wavelength, intensity or type of metal.
. What is the range of wavelengths for visible light? Range of frequencies?
Wavelengths: (750 nm - 400 nm) Frequencies: (4x10^14 - 7.5x10^14 Hz)
There are multiple transition series of the hydrogen atom. The Balmer series describes the transitions between the energy level n = 2 and energy levels 3 and above. These transitions occur in the visible range. Below are two other well-known transition series. From which energy levels do these series always originate and in which range of light do these transitions occur?
a. Paschen - originate from n = 3 and occur in the Infrared range b. Lyman - originate from n = 1 and occur in the UV range
You shine 500 nm light on a metal and electrons come off. What will happen if you shine 400 nm light of the same intensity on the metal? a . fewer electrons will come off but with the same velocities b . nothing c . electrons will come off with higher velocities d . the two situations will be identical
c
What did Louis de Broglie propose about matter both large and small?
de Broglie proposed that all matter exhibits wavelike and particlelike behaviors. Larger, slower objects have lower wavelengths than smaller, faster objects.
Aufbau principle
electron configurations in the ground state are built up from the lowest energy levels to higher energy levels.
Hund's Rule
electrons must be placed in separate degenerate orbitals first before pairing.
List the regions of electromagnetic radiation in decreasing order from highest energy to lowest energy.
gamma rays > X-Rays > ultraviolet > visible > infrared > microwaves > radio
If we consider a particle in a one dimensional box, the boundary conditions for the walls is that they have ... potential energy. This means that the probability of finding the particle at the wall is ...
infinite, zero
. Electrons are ... charged and so are attracted to the positive side of a static electric field. In an oscillating electric field, electrons also ...
negatively, oscillate (or vibrate)
The probability function is the wave function squared. By observing the probability functions we can define ... or areas of electron density around the nucleus
orbitals
Erwin Schrödinger derived an equation that provides the infinite number of wave functions and associated energies for very small objects. One way we can begin to understand the importance of his solutions is to consider the ... in a ... model
particle, box
The ultraviolet catastrophe outcomes and the photoelectric effect suggest that light behaves as a
particle.
The idea of wave-particle duality tells us that electrons can behave in way similar to both
particles and waves.
Pauli Exclusion Principle
requires the use of ms as the fourth quantum number.
Young's double slit experiment and the observation of diffraction patterns suggest that light behaves as a
wave.
