Table of contents

0. Math Review31m
- Math Review
  31m
1. Intro to Physics Units1h 29m
2. 1D Motion / Kinematics3h 56m
3. Vectors2h 43m
4. 2D Kinematics1h 42m
5. Projectile Motion3h 6m
6. Intro to Forces (Dynamics)3h 22m
7. Friction, Inclines, Systems2h 44m
8. Centripetal Forces & Gravitation7h 26m
9. Work & Energy1h 59m
10. Conservation of Energy2h 54m
11. Momentum & Impulse3h 40m
12. Rotational Kinematics2h 59m
13. Rotational Inertia & Energy7h 4m
14. Torque & Rotational Dynamics2h 5m
15. Rotational Equilibrium3h 39m
16. Angular Momentum3h 6m
17. Periodic Motion2h 9m
18. Waves & Sound3h 40m
19. Fluid Mechanics4h 27m
20. Heat and Temperature3h 7m
21. Kinetic Theory of Ideal Gases1h 50m
22. The First Law of Thermodynamics1h 26m
23. The Second Law of Thermodynamics3h 11m
24. Electric Force & Field; Gauss' Law3h 42m
25. Electric Potential1h 51m
26. Capacitors & Dielectrics2h 2m
27. Resistors & DC Circuits3h 8m
28. Magnetic Fields and Forces2h 23m
29. Sources of Magnetic Field2h 30m
30. Induction and Inductance3h 38m
31. Alternating Current2h 37m
32. Electromagnetic Waves2h 14m
33. Geometric Optics2h 57m
34. Wave Optics1h 15m
35. Special Relativity2h 10m

1. Intro to Physics Units

Introduction to Units

Physics

1. Intro to Physics Units

Introduction to Units

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5:37 minutes

Problem 21

Textbook Question

X rays with an initial wavelength of $0.900 \times 10^{- 10}$ m undergo Compton scattering. For what scattering angle is the wavelength of the scattered x rays greater by $1.0 percent sign$ than that of the incident x rays?

Verified step by step guidance

Determine the relationship between the change in wavelength (Δλ) and the scattering angle (θ) using the Compton wavelength shift formula: Δλ = (h / (m_e * c)) * (1 - cos(θ)), where h is Planck's constant, m_e is the electron mass, and c is the speed of light.

Calculate the change in wavelength (Δλ) as 1.0% of the initial wavelength: Δλ = 0.01 * 0.900 × 10^-10 m.

Substitute the known values of Δλ, h, m_e, and c into the Compton formula to isolate the term (1 - cos(θ)): (1 - cos(θ)) = Δλ / (h / (m_e * c)).

Solve for cos(θ) using the equation: cos(θ) = 1 - (Δλ / (h / (m_e * c))).

Finally, calculate the scattering angle θ by taking the inverse cosine (arccos) of the result: θ = arccos(cos(θ)).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Compton Scattering

Compton scattering is a phenomenon where X-rays or gamma rays collide with matter, resulting in a change in the wavelength of the radiation. This effect occurs due to the interaction between photons and electrons, leading to the transfer of energy and momentum. The change in wavelength is dependent on the scattering angle, which can be calculated using the Compton wavelength shift equation.

Wavelength Shift

The wavelength shift in Compton scattering refers to the difference in wavelength between the incident and scattered X-rays. It can be quantified using the formula Δλ = λ' - λ = (h/m_ec)(1 - cos(θ)), where h is Planck's constant, m_e is the electron mass, c is the speed of light, and θ is the scattering angle. A 1% increase in wavelength indicates a specific relationship between the initial and final wavelengths that must be calculated.

Scattering Angle

The scattering angle is the angle at which a photon is deflected after colliding with an electron. It plays a crucial role in determining the change in wavelength during Compton scattering. By analyzing the relationship between the scattering angle and the resulting wavelength shift, one can derive the angle that corresponds to a specific increase in wavelength, such as the 1% increase mentioned in the question.

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Textbook Question

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Textbook Question

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Textbook Question

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Textbook Question

Model a hydrogen atom as an electron in a cubical box with side length $L$ . Set the value of $L$ so that the volume of the box equals the volume of a sphere of radius $a = 5.29 \times 10^{- 11}$ m, the Bohr radius. Calculate the energy separation between the ground and first excited levels, and compare the result to this energy separation calculated from the Bohr model.

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Textbook Question

A photon is emitted when an electron in a three-dimensional cubical box of side length $8.00 \times 10^{- 11}$ m makes a transition from the $n sub X equals 2$ , $n sub Y equals 2$ , $n sub Z equals 1$ state to the $n sub X equals 1$ , $n sub Y equals 1$ , $n sub Z equals 1$ state. What is the wavelength of this photon?