With a plane wave, I always took the direction of the wavevector, k, as the direction of propogation (magnitude proportional to the inverse wavelength). Alternatively, it could represent the momentum (minus a factor ?) of a particle.
However inside a crystal, the electron wavevector and the electron velocity are not necessarily in the same direction. I'm thinking here of a 2D material with a cylindrical Fermi surface where the momentum may have a z component, but the Fermi velocity does not. In everyday cases you would expect momentum and velocity to be in the same direction, moreover I considered the propogation of the wave to be in the same direction as its particle analogue.
I realise that inside a crystal the electrons are no longer simple plane waves, but what then does the k vector mean?
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A series RLC circuit consists of a 58.0 ? resistor, a 2.50 mH inductor, and a 450 nF capacitor. It is connected to a 3.0 kHz oscillator with a peak voltage of 5.60 V. What is the instantaneous emf E when i = I ? What is the instantaneous emf E when i = 0A and is decreasing? What is the instantaneous emf E when i = - I ?
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A bullet of mass 2.0×10−3 kgkg embeds itself in a wooden block with mass 0.981 kgkg , which then compresses a spring (kkk = 130 N/mN/m ) by a distance 5.5×10−2 mm before coming to rest. The coefficient of kinetic friction between the block and table is 0.60. a. What is the initial speed of the bullet? b. What fraction of the bullet's initial kinetic energy is dissipated (in damage to the wooden block, rising temperature, etc.) in the collision between the bullet and the block? |
In: Physics
A river has a steady speed of 0.650 m/s. A student swims upstream a distance of 1.00 km and swims back to the starting point.
(a) If the student can swim at a speed of 1.15 m/s in still
water, how long does the trip take? s
(b) How much time is required in still water for the same length
swim? s
(c) Intuitively, why does the swim take longer when there is a
current?
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You hold a ruler that has a charge on its tip 4 cm above a small piece of tissue paper to see if it can be picked up. The ruler has −14 µC of charge. The tissue has 1 g of mass. What is the minimum charge required to pick up the tissue paper?
Answer: ___ µC
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The drawing shows a square, each side of which has a length of L = 0.250 m. Two different positive charges q1 and q2 are fixed at the corners of the square. Find the electric potential energy of a third charge q3 = -3.00 x 10-9 C placed at corner A and then at corner B.
In: Physics
Olive and her friend Wellington are playing down by Captain Don's docks when they find an old chain. The old chain has only three links. By measuring with an old fish scale which is a permanent feature of the dock area, they determine that the total mass of the chain is 2.55 kg (the scale reads in newtons, but Olive knows how to calculate the mass of the chain from its weight). While playing with the scale and the chain (the chain is hanging vertically from the end of the scale, and Olive is holding on to the top of the scale with both hands, either moving the entire system upwards or downwards), Olive notices that if she is accelerating the chain either upwards or downwards, the scale no longer accurately reads the weight of the chain.
When the Scale Reading is Larger than the Weight of the Chain: At one point in their experiments with the chain and the scale, Wellington observes that the scale reads 42.00 N
A: When the scale reads 42.00 N, what is the tension in the chain at the point where the lowest two links connect?
B: When the scale reads 42.00 N, what is the tension in the chain at the point where the topmost two links connect?
C: Consider all the downward forces which are acting on the middle link. When the scale reads 42.00 N, what is the magnitude of the sum of all those downward forces?
When the Scale Reading is Smaller than the Weight of the Chain: At another point in their experiments, Wellington observes that the scale reads only 11.50 N. (We could ask the same questions for this case as were asked for the case when the scale read 42.00 N. Instead, to further test your understanding, we will ask a slightly different set of questions.)
D: When the scale reads 11.50 N what is the Up-Down component of the acceleration of the old chain? Let Up be positive.
E: When the scale reads 11.50 N what is the Up-Down component of the force on the lowest link by the middle link? Let Up be positive.
F: Consider all the downward forces which are acting on the middle link. When the scale reads 11.50 N, what is the magnitude of the sum of all those downward forces?
Using the Chain to Tow a Sled: Old Captain Don is overjoyed when he sees the kids playing with the chain, because he had lost the chain sometime last winter. It turns out that Captain Don uses the chain to connect his snowmobile to his homemade sled in which he tows loads of fish, or ice, or supplies, etc. back and forth from his nearby house and office to his dock in the wintertime. Assume, for the purposes of this problem, that the little homemade sled slips across the winter snows with little friction of any kind. Suppose the mass of the sled and its load is 33.00 kg, and suppose that Captain Don is speeding up on level ground at a rate of 39.00 cm/s2 cm/s2 as he is just starting out on a towing trip. Also, assume that the chain stretches horizontally from a hook on the snowmobile to a hook on the homemade sled, i.e. ignore any sagging in the chain which is connecting the snowmobile to the homemade sled.
G: What is the tension in the chain at the meeting of links which is closest to the sled?
H: What is the tension in the chain at the meeting of links which is closest to the snowmobile?
In: Physics
Niels Bohr
a.) A dense explanation of the Bohr model. explanations of practicum used, derivations, and examples.
b.) Has future work disproven/improved/built on this discovery?
c.) how is this discovery important?
In: Physics
Light strikes a flat piece of uniformly thick glass at an incident angle of 60?. If the index of refractino of the glass is 1.5, and it has a width of 10 cm,
A) What is the angle of refractino in the glass?
B) What angle will the light leave the glass at on the other side?
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1. A healthy diastolic blood pressure at the level of
the heart is about 104 Pa. Assuming blood has a density of 1.1
g/cm3, what is the diastolic blood pressure in the feet of a
standing person if his heart is 1.4 m above the ground?
A) 104 Pa
B) 1.1 104 Pa
C) 1.4 104 Pa
D) 1.5 104 Pa
E) 1.6 104 Pa
2. A horizontal pipe has a part with a diameter 1/3 of
the rest of the pipe. If v is the speed of the fluid in the wider
section, then the speed in the narrower section is:
A) v/9
B) v/3
C) v
D) 3v
E) 9v
3. The part of an iceberg that extends above the water
for ice density of 0.9g/cm3 and salted water of 1.1 g/cm3 is
A) 9%.
B) 18%
C) 20%
D) 80%.
E) 82%
F) 91%
4. The weight of a solid metal object in air is 25 N
and the apparent weight in water (=1g/cm3) is 20 N. It's density
is
A) 1 g/cm3
B) 2 g/cm3.
C) 5 g/cm3
D) 10 g/cm3
E) 20 g/cm3
10-14. A 2 kg object in simple harmonic motion obeys
the following position versus time equation: y = (0.25 m) sin
(πt).
10. What is the amplitude of vibration?
A) 0.25 m
B) 0.50 m
C) 0.75 m
D) 1.0 m
E) 0.5 π m
11. What is the frequency of the vibration?
A) 0.25 Hz 2πft = πt
B) 0.50 Hz
C) 1 Hz
D) 4 Hz
E) 0.5 π Hz
12. What is the maximum velocity ?
A) 0.25 m/s
B) 0.50 m/s
C) 1.0 m/s
D) 0.25 π m/s
E) 0.5 π m/s
13. What is the total energy of the system?
A) 1.23 J
B) 2.46 J
C) 4.92 J
D) 9.9 J
E) 0 J
14. What is the magnitude of the force acting on the
mass after 2 s ?
A) 1.23 N
B) 2.13 N
C) 2.46 N
D) 4.92 N
E) 0 N
In: Physics
A flat square sheet of thin aluminum foil, 30 cm on a side, carries a uniformly distributed 285 nC charge.
Part A What, approximately, is the electric field 1.0 cm above the center of the sheet? Express your answer using two significant figures.
What, approximately, is the electric field 20 mm above the center of the sheet? Express your answer using two significant figures.
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A parallel-plate capacitor has capacitance C = 15.7 pF when the volume between the plates is filled with air. The plates are circular, with radius 2.50 cm. The capacitor is connected to a battery and a charge of magnitude 28.0 pC goes into each plate. With the capacitor still connected to the battery, a slab of dielectric is inserted between the plates, completely filling the space between the plates. After the dielectric has been inserted, the charge on each plate has magnitude 45.0 pC.
(a) What is the dielectric constant K of the dielectric?
(b) What is the potential difference between the plates before and after the dielectric has been inserted?
(c) What is the electric field at a point midway between the plates before and after the dielectric has been inserted?
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Show that an atom with a filled subshell must have a 1S0 ground state.
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A man is hiking at a park. At the beginning, he followed a straight trail. From the starting point, he traveled two miles down the first trail. Then he turned to his left by 30 degree angle to follow a second trail for one point five miles. Next, he turned to his right by 160 degree angle and follow a third trail for one point seven miles. At this point he was getting very tired and would like to get back as quickly as possible, but all of the available trails seem to lead him deeper into the woods. He would like to take a shortcut directly through the woods. How far to his right should you suggest him to turn, and how far do he have to walk, to go directly back to his starting point?
Q1: The man has to turn ____ degree to the right and walk ___ miles to the starting point.
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