Particle Nature of Light. Wave-Particle Duality. KE max

Transcription

1 Particle Nature of Light h f = KE max + W o KE max Wave-Particle Duality λ=h/mv Complete the following statement: According to the de Broglie relation, the wavelength of a "matter" wave is inversely proportional to (a)planck's constant. (b) the frequency of the wave. (c) the mass of the particle. (d) the speed of the particle. (e) the momentum of the particle. X What happens to the de Broglie wavelength of an electron if its momentum is doubled? (a) The wavelength decreases by a factor of 4. (b) The wavelength increases by a factor of 2. (c) The wavelength increases by a factor of 4. (d) The wavelength decreases by a factor of 2 X (e) The wavelength increases by a factor of 3. Determine the de Broglie wavelength of a neutron (m = kg) that has a speed of 5.0 m/s. (a) 79 nm X (b) 395 nm (c) 1975 nm (d) 162 nm (e) 529 nm Upon which one of the following parameters does the energy of a photon depend? (a) mass (c) polarization (e) phase relationships (b) amplitude (d) frequency X For which one of the following problems did Max Planck make contributions that eventually led to the development of the quantum hypothesis? (a) photoelectric effect (d) the motion of the earth in the ether (b) uncertainty principle (e) the invariance of the speed of light through vacuum (c) blackbody radiation curves X Light is usually thought of as wave-like in nature and electrons as particle-like. In which one of the following activities does light behave as a particle or does an electron behave as a wave? (a) A Young s double slit experiment is conducted using blue light. (b) X-rays are used to examine the crystal structure of sodium chloride. (c) Water is heated to its boiling point in a microwave oven. (d) An electron enters a parallel plate capacitor and is deflected downward. (e) A beam of electrons is diffracted as it passes through a narrow slit. X

2 Wave Function, ψ Type of waves Water waves Sound waves Light waves Matter waves Description of waves Variable physical quantity Height of the water surface Pressure in the medium Electric and magnetic fields Wave function, Ψ Ψ, the amplitude of a matter wave, is a function of time and position Probability Density Ψ 2 The value of Ψ 2 for a particular object at a certain place and time is proportional to the probability of finding the object at that place at that time. For example: Ψ 2 =1: the object is definitely there Ψ 2 =0: the object is definitely not there Ψ 2 =0.4: there is 40% chance of finding the object there at that time. Ψ 2 starts from Schrodinger s equation, a differential equation that is central to quantum mechanics Why Ψ 2? Why not Ψ? Amplitude of every wave varies from A to +A to A to +A and so on (A is the maximum absolute value whatever the wave variable is). A negative probability is meaningless. Ψ 2 gives a positive quantity that can be compared with experiments. The key point to the wave function is that the position of a particle is only expressed as a likelihood or probability until a measurement is made.

3 The probability the electron will be found at the particular position is determined by the wave function illustrated to the right of the aperture. When the electron is detected at A, the wave function instantaneously collapses so that it is zero at B. Question: A large value of the probability density Ψ 2 of an atomic electron at a certain place and time signifies that the electron (a) is likely to be found there (b) is certain to be found there (c) has a great deal of energy there (d) has a great deal of charge there Answer: a Question: A moving body is described by the wave function Ψ at a certain time and place. The value of Ψ 2 is proportional to the body s a. electric field. b. speed c. energy d. probability of being found Question: What do physicists enjoy the most at baseball games? Answer: The wave. Answer: d 1. If an object has a well-defined position at a certain time, its momentum must have a large uncertainty. 2. If an object has a well-defined momentum at a certain time, its position must have a large uncertainty.

4 Uncertainty Principle Momentum and position ΔxΔp h/4π Energy and time ΔEΔt h/4π p=h/λ precise x unknown Δx better defined (narrower wave packet) Δp less defined (greater spread of λ) Uncertainty principle ΔxΔp h/4π In the microscopic world where the wave aspects of matter are very significant, these wave aspects set a fundamental limit to the accuracy of measurements of position and momentum regardless of how good instruments used are. The uncertainty principle is the physical law which follows from the wave nature of matter Example: Compare the de Broglie wavelength of 54-eV electrons with that of a 1500-kg car whose speed is 30 m/s. Solution: For the 54-eV electron: KE=(54eV)(1.6x10-19 J/eV)=8.6x10-18 J KE=1/2 mv 2, mv=(2mke) 1/2 λ=h/mv=h/(2mke) 1/2 = 1.7x10-10 m The wavelength of the electron is comparable to atomic scales (e.g., Bohr radius=5.29x10-11 m). The wave aspects of matter are very significant. For the car: λ=h/mv=6.63x10-34 J s/(1.5x10 3 )(30m/s)= 1.5x10-38 m The wavelength is so small compared to the car s dimension that no wave behavior is to be expected. Question: The narrower the wave packet of a particle is a. the shorter its wavelength b. the more precisely its position can be c. the more precisely its momentum can be d. the more precisely its energy can be Answer: b Question: The wave packet that corresponds to a moving particle a. has the same size as the particle b. has the same speed as the particle c. has the speed of light d. consists of x-ray Answer: b

5 Question: If Planck s constant were larger than it is, a. moving bodies would have shorter wavelength b. moving bodies would have higher energies c. moving bodies would have higher momenta d. The uncertainty principle would be significant on a larger scale of size If Planck s constant were changed to 660 J s, what would be the minimum uncertainty in the position of a 120-kg football player running at a speed of 3.5 m/s? (a) m (b) 0.13 m (c) 0.50 m (d) m (e) 0.25 m X Answer: d