Chapter 17 - Quantum Mechanics

What was Einstein's explanation of the photoelectric effect?

1) Einstein used the photoelectric effect as a test for Planck's quantum hypothesis involving "Blackbody radiation". 2) His proposal: that the energy of light is not transmitted in a continuous wave, but rather is concentrated in bundles of energy he called PHOTONS. Further, he proposed that the amount of energy in each of these bundles is DISCRETE: a fixed amount determined by Planck's equation E=hf. 3) The energy of a photon is QUANTIZED and depends on its FREQUENCY. 4) An electron is ejected from the metal by a collision with a single photon. Each photon needs enough energy to knock an electron free. The minimum energy is the work required to release the electron from its metal atom= Work Function. Increasing the intensity of low-frequency light would only create more photons per second but they would still each only have the same amount (quanta) of energy. 5) Electrons are only removed if the photon has enough energy (E=hf) to overcome the work function. Energy is required to do the work of liberating electrons.

What is a black body and what is black body radiation?

1. A black body is an object that absorbs all radiation that falls on it. 2. It is an excellent absorber (and therefore and excellent emitter). 3. A blackbody will emit radiation (called blackbody radiation) more efficiently than any other object. 4. It's called black body radiation because it is the radiation that is emitted by the object itself and not that which is reflected off it.

What is the relationship between intensity of radiation, wavelength, and temperature? (2)

1. As intensity (amount of radiation emitted) increases, temp of black body increases. 2. As temp increases, the peak shifts to the left= smaller wavelengths, higher frequencies.

What is the 1 problem with the Classical Wave Theory of light?

1. Classical wave theory suggests that light energy can occur at any value and is dependant on amplitude and frequency. Problem 1: This is not the case. Bright, powerful (high amplitude) spotlights do not give us sunburns but high frequency UV light does. New hypothesis 1: Energy is quantified (discrete). (Planck)

What is the Compton effect and what did he find?

1. Compton directed a beam of x-rays at a thin foil target made of carbon and found that the x-ray photons were deflected in many different directions (scattering). 2. Compton measured the energies of these photons and found that they were different from the incident x-ray photons. Also, electrons were ejected from the foil. 3. Summary: The increase of wavelength of x-rays after collision with electrons.

Describe how the Compton effect fits the conservation of energy.

1. E of initial photon = E emitted photon + KE electron 2. E x-ray = hf + 1/2mv^2

What are the experimental findings of the photoelectric effect?

1. Electrons are emitted from the photoelectric surface only when the light is above a certain frequency, f, called the THRESHOLD FREQUENCY. 2. For a given frequency of light (>f) the kinetic energy of the ejected electrons was the same. Increasing intensity (brightness) of the light caused more ejected electrons but their individual kinetic energy did not increase. 3. If same frequency of light was shone on different types of metal cathode, the kinetic energy of the ejected electrons depended on the type of metal. Different metals required different amounts of energy to liberate an electron. This energy is known as the WORK FUNCTION (W). 4. The intensity of the light has no effect on the threshold frequency. No matter how intense the incident light is, if it is below the threshold frequency no electrons will be ejected. 5. If different frequencies of light (>f) are directed at the same surface, the kinetic energy of the ejected electrons varies with frequency. Higher frequency light gives electrons more kinetic energy.

What are 3 important notes on light?

1. Light in its interactions with matter has discrete energy values. It can behave like a stream of particles which have wave properties such as frequency, diffraction etc. 2. Light is viewed as an electromagnetic wave but it shows particle properties in some cases; (black body radiation, photoelectric effect, Compton effect) 3. This is often referred to as the wave-particle duality of light.

What are the 4 basic ideas of Bohr's theory?

1. The electron moves in a circular orbit around the proton under the influence of the Coulomb force of attraction. 2. Only certain orbits are stable. These orbits are ones in which the electron does not emit energy in the form of radiation. 3. Radiation is emitted by the atom when the electron jumps from a higher to lower orbit. The frequency of the emitted photon is related to the change in the atoms energy. It is independent of the frequency of the electrons orbital motion. 4. The size of the allowed electron orbits is determined by a condition imposed on the electron's orbital angular momentum.

What are the 3 types of radiation given off for the 3 types of temperatures?

1. Warm objects (>35ºC) give off mostly infrared radiation. We feel it but cannot see it. 2. Hot objects (>700ºC) give off mostly infrared but begin to emit some red glow. 3. Very hot objects (>3000ºC) give off mostly visible and thus have a white glow.

What is the 2 problem with the Classical Wave Theory of light?

2. Classical wave theory suggests that light energy has no mass and therefore no momentum. Problem 2: Wrong. Compton (1923) noted that x-rays have momentum, they eject electrons from metal. But where did the electron get momentum from? Is conservation of momentum valid? New hypothesis 2: Light has momentum (waves exhibit particle properties).

What is the 3 problem with the Classical Wave Theory of light?

3. Classical wave theory suggests that forms of energy can exhibit wave properties, however, particles (matter) will not exhibit wave properties. Problem 3: Wrong. Electrons, protons and neutrons (particles) all have shown diffraction in lab experiments, a characteristic of waves. New hypothesis 3: Atomic particles exhibit wave properties (de Broglie).

What happens when an electron drops from a higher energy level to a lower energy level?

It emits a photon (energy).

What is the 4 problem with the Classical Wave Theory of light?

4. Classical physics suggests that a moving charge (with changing velocity vector) will produce electromagnetic radiation. Thus, electrons orbiting an atom should lose energy, as they emit EM radiation, and fall into the nucleus. Problem 4: Wrong. Most atoms are stable. New hypothesis 4: Neutral atoms are stable. Electrons have certain orbit levels and only release radiation/energy when they drop to a given lower level. The released energy is quantized since the orbit levels of a specific atom are at fixed increments (Bohr).

Explain black body radiation.

Any opaque object with a temperature above absolute zero radiates photons, packets of electromagnetic radiation. The radiation is sometimes referred to as thermal radiation. An obvious example is a hot stove element glows in the dark. As an object is heated, radiation is emitted from the infrared, visible and UV portions of the EM spectrum.

When does the electron's orbit have the smallest radius - and what is this called?

Bohr radius: n=1, r= 5.29x10⁻¹¹m

How do you find the energy of the photon emitted/ absorbed when an electron jumps/drops from upper to lower?

Calculate each energy and subtract. *** n upper > n lower.

What was the classical wave theory's problem with the photoelectric effect?

Classical: there is no reason why an intense beam of low-frequency light cannot produce a photoelectric current, or why the intensity of the beam does not affect the kinetic energy of the ejected electrons. Photoelectric effect says different: classical wave theory could not explain.

What does the Compton effect show?

Compton effect: the increase in wavelength of x-rays after collision with electrons. Shows: Photons have momentum! More support for the idea that light possesses both wave and particle properties.

What does the quantized electron energy for the orbital levels of an element depend on?

Depends on the difference between energy levels.

Explain the equation Ephoton = Ek + Wo.

Ephoton = incident photon Ek= kinetic energy of the electrons Wo = Work function of the metal

What condition must we have for the photoelectric effect to occur?

Ephoton > Wo!

Explain phosphorescence.

Ex: luminous watch dial. Atoms are excited by absorption of a photon to an energy level said to be metastable. When an atom is raised to a normal excited state, it drops back down very quickly. Metastable states last a few seconds or longer. In a collection of atoms, many of these atoms will remain in the excited state for over an hour - light will be emitted after even longer periods.

Explain fluorescence.

Ex: trail marker tape used in hiking trails and road signs. When atom is excited from one energy state to a higher one by absorption of a photon, it may return to the lower level in a series of 2 or more jumps. The emitted photons will have lower energy and frequency than the absorbed photon. When absorbed photon is in the UV region and the emitted photon is in the visible region of the spectrum = fluorescence.

Describe how the Compton effect fits the conservation linear momentum.

P initial photon = P emitted photon + P electron

Explain the equation P= h/lambda

P= h/lambda P = momentum "Comptons photon momentum equation"

What happens when a high voltage is applied across a gas discharge tube?

Radiation from the excited gases produces a line spectrum (only certain wavelengths).

Why does radiation happen?

Radiation is due to the oscillation of electric charges in the molecule.

What is an electron volt?

Small amounts of energy are often expressed with eV's. 1 eV = 1.6 x 10⁻¹⁹ J

Why don't electrons spiral into the nucleus?

The electron has negative energy - like it is in a hole in the ground. It would need to gain energy to escape the hole. Lower electron is in the hole - lower the energy. Must gain energy to jump to a higher orbital level.

explain the threshold frequency (fo).

The electron has to receive the minimum amount of energy (Wo) to escape the attractive forces holding it to the metal. When the frequency of the incident light is too low, the photon does not give electron enough energy to leave the surface.

Explain emission spectra:

The electrons exist at certain quantized energy levels. As an electron drops from a high energy level to a lower one it will release energy in the form of a photon. Since these energy levels (shelves) can only exist at certain levels, the emitted wavelength of light can only exist as certain whole numbers as well.

What is an important note about these lines spectra?

They are always the same wavelength for a given gas - its like an atomic fingerprint !!

What is important to remember about Planck's equation, E=hf?

This is the smallest amount of energy that can be transferred for a given wavelength of EM radiation.

How do you measure the kinetic energy of the ejected electrons during the photoelectric effect?

To measure the kinetic energy of the ejected electrons, the polarity of the potential (power supply) can be reversed and then varied. If the reversed potential is slowly increased until the electrons stop flowing, this stopping potential (Vstop) must balance the electrons kinetic energy.

What is the photoelectric effect?

a phenomena that occurs when light shone on a metal surface causes electrons to be emitted from the metal.

What is FLUX?

energy flow per unit area.

What is the formula for cutoff frequency? How do you get this?

fo= Wo / h you get this by setting Ek=0

What does "discrete" mean?

individually separate and distinct.

What is quantum theory?

is the theory of how atoms, matter and energy are interrelated.

What is a good approximation of a black body?

light enters an opening, hits a wall, some is absorbed and some is reflected until all the light is absorbed.

What is absorption spectra?

the dark lines which are observed when a continuous spectrum passes through a gas. These lines have the same wavelength as the emission lines from that gas.

Define Ionization energy.

the magnitude of energy needed to remove an electron completely from the nucleus (r=infinity).

What is the stopping potential?

the minimum potential (voltage) to prevent electrons from being ejected from the metal.

What is emission spectra?

the spectrum lines which are created from an excited gas.

What is the ground state?

when n=0.

How do you get the orbital radius for the hydrogen atom? What does this represent?

where n = quantum # / orbital level rn = allowed orbits for an electron - radii have discrete values.

What is a nanometre?

x 10⁻⁹ m

What is a picometre?

x10⁻¹²