Final Exam (ch.13-ch.19) . time: Thu 05/03   10:20 am- 12:20 pm . Location: room 114 of physics building. If you can not make it, please let me know by Wednesday 04/25 so that I can arrange a make-up exam. If you have special needs, e.g. exam time extension, and has not contact me before, please bring me the letter from the Office of the Dean of Students before Wednesday 04/25. No requests will be accepted after that. AOB •30  problems. •Prepare your own scratch paper, pencils, erasers, calculators etc. •Use only pencil for the answer sheet •No cell phones, no text messaging which is considered cheating. •No crib sheet of any kind is allowed. Equation sheet will be provided and will also be posted on the web.

A chain reaction can thus release enormous quantities of energy. Each of these fission reactions is initiated by a neutron, and each reaction emits several more neutrons. These neutrons can then initiate more fission reactions, etc.  Chain Reactions. A chain reaction can thus release enormous quantities of energy. But achieving a chain reaction is difficult. Natural uranium is only 0.7% U-235; it is mostly U-238, which absorbs neutrons without fission. If too many neutrons are absorbed or escape, the chain reaction dies.

Fusion Each fusion produce 17.6 MeV = 17.6× 10 6 𝑒𝑉 ×1.6× 10 −19 J = 2.8× 10 −12 J Each fission ~ 200 MeV = 3.2× 10 −11 J Which is larger but a single U235 has a lot more nucleons than deuterium and tritium. Under the same mass, fusion will produce much more powerful energy than fission.

How much U-235 is needed to build a fission bomb as powerful as 20kiloton TNT ? 20 𝑘𝑖𝑙𝑜𝑡𝑜𝑛=8.4× 10 13 𝐽. Each fission = 3.2× 10 −11 J One needs 2.6× 10 24 𝑓𝑖𝑠𝑠𝑖𝑜𝑛𝑠, 𝑖.𝑒. 𝑈 235 𝑎𝑡𝑜𝑚𝑠. that is 2.6× 10 24 /6.02× 10 23 moles=4.3 moles M(U235) is 235 g/mole, which leads to 1kg U235.

This pattern of oscillation is called a standing wave. The waves traveling in opposite directions interfere in a way that produces a standing or fixed pattern. The distance between adjacent nodes or adjacent antinodes is half the wavelength of the original waves. At the nodes, it is not moving at all. At points between the nodes and antinodes, the amplitude has intermediate values.

Real Musical Instrument 4B-10 MONOCHORD What is the purpose of tightening or loosening the string ? What role do the frets play ? Real Musical Instrument Chinese Zither Each wire also passes over a small wooden bridge that can be moved back and forth tightening or loosening the string A high pitch sound corresponds to a high frequency sound wave and a low pitch sound corresponds to a low frequency sound wave CHANGING TENSION OF THE STRING AFFECTS THE SPEED OF WAVE PROPAGATION AND CHANGES THE FUNDAMENTAL FREQUENCY THE BRIDGE ACTS AS A FRET THAT EFFECTIVELY CHANGES THE LENGTH OF THE WIRE AND THE FUNDAMENTAL FREQUENCY 12/5/2018

Electromagnetic Waves An electromagnetic wave consists of time-varying electric and magnetic fields, in directions perpendicular to each other as well as to the direction the wave is traveling.

Why is the sky blue? The white light coming from the sun is actually a mixture of light of different wavelengths (colors). The shorter wavelengths of blue light are scattered by gas molecules in the atmosphere more than longer wavelengths such as red light. The blue light enters our eyes after being scattered multiple times, so appears to come from all parts of the sky.

Why is the sunset red? The shorter wavelengths of blue light are scattered by gas molecules in the atmosphere more than longer wavelengths such as red light. When the sun is low on the horizon, the light must pass through more atmosphere than when the sun is directly above. By the time the sun’s light reaches our eyes, the shorter wavelengths such as blue and yellow have been removed by scattering, leaving only orange and red light coming straight from the sun.

Quiz (Bonus): Is it possible for an electromagnetic wave to travel through a vacuum? A. Yes. B. No. Quiz (bonus): Waves are traveling in an eastward direction on a lake. Is the water in the lake necessarily moving in that direction? Yes. No. Water moves up and down.

Quiz (bonus): A wave can be propagated on a blanket by holding adjacent corners in your hands and moving the end of the blanket up and down. Is this wave transverse or longitudinal? Longitudinal Tranverse. Quiz (Bonus) A band playing on a flat-bed truck is approaching you rapidly near the end of a parade. Will you hear the same pitch for the various instruments as someone down the street who has already been passed by the truck? A. The pitch increases as the band approaches and decreases as it is going away B. The pitch decreases as the band approaches and increases as it is going away C. The pitch remain unchanged.

Quiz (Bonus): What is the frequency of light waves with a wavelength of 6 x 10-7 m? 1 x 1014 Hz 3 x 1015 Hz 2 x 1012 Hz 5 x 1014 Hz 7 x 107 Hz  = 6 x 10-7 m f = v /  v = c = 3 x 108 m/s = (3 x 108 m/s) / 6 x 10-7 m v = f  = 5 x 1014 Hz

7A-21 Refraction

Speed of light in medium Light can travel through matter medium as well as free space (vacuum). Inside matter, the speed of light v is generally less than c. index of refraction When light encounters an interface between different media, it can generally both reflect and refract.

Law of reflection and Refraction 𝜃 1 = 𝜃 1 ′ medium n vacuum 1 air 1.0003 water 1.33 glass 1.5 – 1.66 Snell’s Law

Exercise The refraction index for air and glass are 1.0 and 1.5, respectively. The incident angle θ1 is 30o, what are the reflection angle θ’1 and refraction angle θ2 ? A). θ’1 =30o and θ2=19.5o B). θ’1 =30o and θ2=15o C). θ’1 =19.5o and θ2=30o D). θ’1 =15o and θ2=19.5o E). θ’1 =30o and θ2=22.5o 𝜃 2 = asin sin 30 1.5 =19.5 𝑑𝑒𝑔𝑟𝑒𝑒

Total Internal Reflection All light can be reflected, none refracting, when light travels from a medium of higher to lower indices of refraction. medium 2 medium 1 e.g., glass (n=1.5) to air (n=1.0) But  cannot be greater than 90 ! In general, if sin 1 > (n2 / n1), we have NO refracted ray; we have TOTAL INTERNAL REFLECTION. Critical angle above which this occurs.