Quantum mech
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This document contains 6 physics problems related to quantum mechanics. Problem 1 calculates the number of photons needed to equal the energy of one gamma ray photon. Problem 2 gives the formula for photon energy in terms of wavelength and calculates the visible light photon energy range. Problem 3 finds the wavelength of an incident photon that gives an electron 35 keV of energy during Compton scattering. Problem 4 calculates the percent change in photon energy for different wavelength photons during Compton scattering. Problems 5 and 6 calculate de Broglie wavelengths and position uncertainties. The last problem finds the first three energy levels of a marble and electron confined in boxes.
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Ph 101-7 WAVE PARTICLES
[1] Photoelectric effect provides evidence that light behaves as particles called photons, with each photon having energy hν. This explains the threshold frequency and instantaneous emission.
[2] Compton scattering demonstrates that photons transfer discrete packets of energy and momentum to electrons during collisions, with the photon's wavelength increasing in accordance with conservation laws. This provided direct evidence that photons are real particles.
[3] Pair production demonstrates that a photon's energy can be converted into an electron-positron pair, as predicted by Einstein's equation E=mc2. A minimum photon energy of 1.02 MeV is required to produce the pairs.
Quantum mechanics I
CLASSICAL MECHANICS - FAILURES - PHOTOELECTRIC EFFECT- COMPTON EFFECT - DAVISON AND GERMER EXPERIMENT - HEISENBERG UNCERTAINTY PRINCIPLE - QUANTUM MECHANICS POSTULATES - OPERATORS - COOMMUTATORS
Homework of chapter 40
The document contains multiple questions about modeling the hydrogen atom and particles in boxes using quantum mechanics. It asks the learner to calculate properties like energy levels, transition wavelengths, and tunneling probabilities for various scenarios involving particles in boxes and wells with different widths and depths. It also contains questions about harmonic oscillators and transition energies.
Magnetic effect of_current
This document provides information on the dual nature of matter and radiation, including photoelectric effect questions and answers. It discusses key concepts such as:
- The photoelectric effect and how an uncharged zinc plate becomes positively charged when irradiated by ultraviolet radiation.
- Graphs showing the relationship between photoelectric current and anode potential when frequency is kept constant.
- Questions regarding the wave-particle duality of matter and radiation, including the de Broglie wavelength equation.
- Multi-part questions analyzing graphs and equations related to the photoelectric effect and Einstein's photoelectric equation.
Magnetic effect of_current
This document discusses the dual nature of matter and radiation, including photoelectric effect and de Broglie wavelength. It provides 5 one-mark questions and answers on topics like photoelectric effect and characteristics of incident radiation. It also gives 5 two-mark questions and answers exploring topics such as kinetic energy relationship between an electron and alpha particle with the same de-Broglie wavelength. Finally, it provides 5 three-mark questions and answers examining Einstein's photoelectric equation and variations in photoelectric experiments.
QM tutorial 1_new.pdf
1) The document discusses the concept of de Broglie wavelength and uses examples to calculate the wavelength of a golf ball and electron moving at given velocities.
2) It then discusses several problems involving calculating kinetic energy, momentum, and phase/group velocities of particles like protons and electrons using their de Broglie wavelengths and relativistic equations.
3) The document also summarizes the Davisson-Germer experiment that provided direct evidence of the wave nature of electrons by observing diffraction peaks matching the wavelengths calculated from de Broglie's equation.
6) A beam of light with red and blue components of wavelengths.docx
6) A beam of light with red and blue components of wavelengths 670 nm and 425 nm,
respectively, strikes a slab of fused quartz at an incident angle of 30o. On refraction, the
different components are separated by an angle of 0.001312 rad. If the index of
refractions of the red light is 1.4925, what is the index of refraction of the blue light?
Week 5 Assignment
Early Quantum Theory
Please solve the following problems. You must show all work for full/partial credit.
When complete, attach a typed cover sheet and submit to the assignment drop-box.
1) The walls of a blackbody cavity are at a temperature of 27o C. What is the frequency
of the radiation of maximum intensity?
2) Assume that a 100 – W light bulb gives off 2.50% of its energy as visible light. How
many photons of visible light are given off in 1.00 min? (Use an average visible
wavelength of 550 nm)
3) What is the energy of photons (joules) emitted by an 107.5-MHz FM radio station?
4) What is the longest wavelength of light that will emit electrons from a metal whose
work function is 3.50 eV?
5) A metal with a work function of 2.40 eV is illuminated by a beam of monochromatic
light. If the stopping potential is 2.5V, what is the wavelength of the light?
6) What is the de Broglie wavelength of a 1000 kg car moving at a velocity of 25 m/s?
7) A hydrogen atom in its ground state is excited to the n = 5 level. It then makes a
transition directly to the n = 2 level before returning to the ground state.
a) What are the wavelengths of the emitted photons?
b) Would any of the emitted wavelengths be in the visible region?
8) What is the longest wavelength light capable of ionizing a hydrogen atom in the
ground state?
Week 6 Assignment
Quantum Mechanics of Atoms
Please solve the following problems. You must show all work for full/partial credit.
When complete, attach a typed cover sheet and submit to the assignment drop-box.
1) What is the minimum uncertainty in the velocity of an electron that is known to be
somewhere between 0.050 nm and 0.10 nm from a proton?
2) The energy of the first excited state of a hydrogen atom is -0.34 eV ± 0.0003 eV.
What is the average lifetime of for this state?
3) Knowing that a free neutron has a mean life of 900 s and a mass of m = 1.67 x 10-
27kg, what is the uncertainty in its mass in kg?
4) For n = 5, l = 4, what are the possible values of and ml and ms?
5) Draw the ground state energy level diagrams for nitrogen (N) and potassium (K).
6) Calculate the magnitude of the angular momentum of an electron in the n = 7, l= 5
state of hydrogen.
Week 7 Assignment
Nuclear Physics
Please solve the following problems. You must show all work for full/partial credit.
When complete, attach a typed cover sheet and submit to the assignment drop-box.
1) What is the approximate atomic radius of
2) What is the approximate radius of a nucleus?
(b) Approximately what is the value.
Solid State Physics Assignments
Solid state physics course assignments submitted by Deepak Rajput at the University of Tennessee Space Institute at Tullahoma in Fall 2006.
Similar to Quantum mech (19)
Thesis on the masses of photons with different wavelengths.pdf
Thesis on the masses of photons with different wavelengths.pdf
6) A beam of light with red and blue components of wavelengths.docx
6) A beam of light with red and blue components of wavelengths.docx
Quantum mech
- 1. Quantum Mechanics 1. How many Photons of red light λ = 6.7× have the same energy as one Photon of γ-rays λ =1. 6.× Sol. = Let n be the required no. of photons of red light which have the same energy as that of one photon of γ-rays, then = 2. Show that the energy of a photon of wavelength λ is given by . Find the range of photon energies in the visible portion of electromagnetic spectrum. Sol. = =12422/λ The Wavelength range for visible light is 4000-7000 Therefore range of energies for visible photons as 1.8 to 3.1 eV 3. The maximum energy given to an electron during Compton scattering is 35 KeV. Find the wavelength of the incident photon. Sol. The maximum energy is given to an electron when photon is backscattered, that is when . = =0.048 . The energy gained by the electron = energy of the incident photon - energy of the scattered photon =
- 2. Or 4. Calculate the percent change in photon energy for a Compton collision with scattering angle equal to for the radiation in (a) the microwave range, with λ=3.0 cm, (b) the visible range, with λ = 5000 , (c) the X-ray range, with λ =1 and (d) the γ- ray range, with λ = 0.012 . Sol. Fractional loss of energy = = Thus the percentage change in photon energy Therefore the percentage change in photon energy for the radiation in (a) the microwave range, with λ=3.0 cm =8 . (b) The visible range, with λ = 5000 , =5 (c) The X-ray range, with λ =1 =2.3 (d) The γ-ray range, with λ = 0.012 . =66.7 5. Calculate the de Broglie wavelength of (a) a rock of mass 50 g thrown with the speed of 40 , and (b) an electron accelerated through 50 V. Sol. (a) for a rock, λ= =3.31 (b) For an electron,
- 3. λ= 6. Find the uncertainty in position for (a) a ball of mass 45 g with a speed of 40 m/s measured to a precision of 1.5% and (b) an electron moving with a speed of m/s, measured to a precision of 1.5%. Sol. (a) (b) P = 9.1 =1.82 Hence 10 Find the first three energy levels of (a) a marble of mass 10 g in a box of width 10 cm and (b) an electron in a box of width 1Å.` Sol. The marble or electron cannot leave the box, therefore the problem is like that of a particle in an infinite potential well. The energy level is given by (a) For a marble =5.5 Thus (b) For an electron
- 4. Thus