The density of sodium is 0.971 g/cm3 and it has an atomic weight of 22.9897 g/mol. Each sodium atom contributes one valence electron to the metal, so the number of electrons per unit volume, N/V, is equal to the number of sodium atoms per unit volume.

   a) Calculate the number density of atoms per unit volume, N/V.    b) Calculate the Fermi energy of sodium.    c) Calculate the Fermi temperature.   d) At room temperature (298 K), calculate the chemical potential.   e) Calculate the degeneracy pressure for the electron gas.

Match each passage with the title of the poem from which it is taken.

Pat, Shannon and Fido (their dog) are on a circular path 100 feet around. Fido is very excited. Shannon starts walking around the path maintaining a speed of 1 foot per second, while Pat stays still. Fido begins racing back and forth between Pat and Shannon on the circular path along the section of the path Shannon has NOT walked on. What is Fido’s average speed if he has just returned to Pat for the 5th time when Shannon gets to the half-way point? **IMPORTANT** Assume Fido maintains a constant speed of 3 feet per second for this last run back to Pat. **IMPORTANT** Also, assume that Fido met Shannon at equally spaced moments in time (including the starting).

In a barotropic fluid, why is the change in depth dynamically analogous to a change in the Coriolis parameter (i.e. planetary vorticity)? HINT: Use the concept of the Conservation of Potential Vorticity to help you.

1. Exactly when is the electric power generated that you use in homes in Canada?

2. What is the underlying reason that the typical voltage of most battery cells is in the

   order of some Volts and not significantly higher?

3. Typical metals have an increased resistance at higher temperatures. For a usual

   incandescent light bulb, when does the highest current flow?

1. A typical α-decay from a parent nucleus ^A_ZX may be indicated as :

Group of answer choices

^A_ZX → ^(A−4)_{(Z − 2)} Y + ⁴₂He

^A_ZX → ^(A+4)_(Z+2) Y + ²₂He

^A_ZX → ^(A−4)_Z Y + ⁴₂He

^A_ZX → ^(A−4)_(Z+2) Y + ⁴₂He

2. An element of atomic number 83 in a relatively higher energy state decays radioactively to an element of atomic number 84 with lower energy level. This must include

Group of answer choices

an α emission

a β emission

a γ emission

a β & γ emission

3. The half- life of radium-226 is 1.6 × 10³ . If a sample initially contains 3.0 × 10¹⁶ such nuclei, what is the number of radioactive radium-226 nuclei remaining after 4.8 × 10³ years?

Group of answer choices

2.25 × 10¹²

3.75 × 10¹⁶

2.2 × 10¹⁶

3.75 × 10¹⁵

A) An isolated spherical conductor has an excess charge of -9.8 μC placed on its surface. Inside the conductor is a cavity, within which is a point charge of 4.10 μC. How many excess electrons are on the exterior surface of the conductor?

B) A cubical box has a charge q = -2.1 μC placed at its center. Calculate the electric flux through the right face of the box.

C) A charged ball with a mass of 10.0 g is suspended on a string in a horizontal electric field of 150.0 N/C directed to the right. The string makes an angle of 13.0 deg to the right of vertical. Find the charge carried by the ball.

D)Two charges, q₁ = -16.5 μC and q₂ = -1.5 μC , are located at (x,y) = (13.2, 22.2) cm and (10.6, 16.4) cm respectively. Find the electrostatic force between these two changes (take an attractive force to be negative)

Clark W. Griswold has been banned by his wife Ellen from any more home lighting projects during the holidays… but she never said anything about the car. Clark bought several boxes of 85W light bulbs and wires them into strands of five bulbs each in series.

He then connects the strands to his 12V car battery (in parallel) and tapes them to the body of his station wagon.  How many individual bulbs are used before Clark blows a 5A fuse connected to the battery?

Note: Use 110V for wall voltage.

1. A boat with a mass of 500kg is initially moving at a speed of 20m/s east (+). The kinetic friction force between the hull of the boat and the water has a coefficient of kinetic friction of m=0.05?

   Part A) What is the magnitude and direction of the kinetic frictional force acting on the boat?

   Part B) Oars are then extended and used so that the oars provide a force, F= 503N, in a direction that is 20° south of east. A steady wind pushes the boat at 35° north of east with a constant force, F=300N. What is the net force acting on the boat? (be sure to give magnitude and direction, and to include the kinetic frictional force from part A!)?

   Part C) What is the acceleration of the boat? If you assume the acceleration is constant, what is the boat's velocity 2 seconds later?

1. A star is being observed with an 8 bit CCD has a central pixel value of 82 counts when the exposure time is 10 seconds. What would the central pixel value be if the exposure time were 25 seconds? Explain your reasoning.

   		The central pixel value would be about 82 counts since the detector is linear.
   		The central pixel value would be about 205 counts since the detector is linear.
   		The central pixel value would be about 305 counts since the detector is linear.
   		The central pixel value would be about 159 counts since the detector is linear.

2. A 12-bit CCD collects light from a star over a 10 second exposure and obtains a central pixel value of 1068. What is the longest exposure that could be taken of this star and still avoid saturation? Explain your reasoning.

   		A. The longest exposure is about 39 seconds since the detector is linear and will saturate at 4095 counts.
   		B. The longest exposure is about 38 seconds since the detector is linear and will saturate at 4095 counts.
   		C. The longest exposure is about 40 seconds since the detector is linear and will saturate at 4095 counts.
   		D. The longest exposure is about 37 seconds since the detector is linear and will saturate at 4095 counts.

3. Choose the table which most closely agrees with your answer for the followig question:

   Enter the offsets you obtained for starfield 2 and starfield 3 in the table below.

   		X Offset Y Offset Starfield 2 -35 29 Starfield 3 -14 -20
   		X Offset Y Offset Starfield 2 -35 37 Starfield 3 -14 -20
   		X Offset Y Offset Starfield 2 -14 -20 Starfield 3 -34 30
   		X Offset Y Offset Starfield 2 -35 29 Starfield 3 -18 -15

4. Choose the table below which most closely agrees with your answer for Question 7 of the lab.

   The starfields of the blink comparator contain 5 variable stars. Create different blinking sequences in the simulator to identify the variables and record the x and y locations of the variables on this starfield. One variable star has already been located for you. Note that the coordinates do not need to be exact, you just need to be able to find the stars again in the next simulator

   		X coordinate Y coordinate Variable #1 64 114 Variable #2 24 260 Variable #3 131 201 Variable #4 309 177 Variable #5 331 22
   		X coordinate Y coordinate Variable #1 64 114 Variable #2 124 260 Variable #3 131 201 Variable #4 309 177 Variable #5 331 22
   		X coordinate Y coordinate Variable #1 64 114 Variable #2 124 260 Variable #3 131 201 Variable #4 309 177 Variable #5 350 122

5. Decide if the following answer is true or false for the question:

   Hypothetically, suppose that you add a long series of observations all taken one day apart to the blinking queue. Would you be able to detect large amplitude variable stars with periods of a) 1.0 days, b) 0.5 days, or c) 0.75 days?

   Answer:

   If the observations are taken 1 day apart then you will not see large amplitude variable stars with periods of 1.0 day or 0.5 days because after one day both types of stars will be in the same phase on each day of observation.

   If the star has a period of 0.75 days then the phase will not be the same after one day. A period of 0.75 days is 18 hours. Suppose on the first day the phase of the star is 0. After 18 hours the phase will again be 0 so after 6 more hours the phase will now be 0.33 or 6/18 = 1/3 of a cycle.   On day 2 we have: after another 18 hours the phase will again be 0.33 so after another 6 hours the phase will advance another 1/3 cycle so the phase is 0.67. On day 3 the phase will be back to 0.

   Another way of looking at this is to consider when the phase will be 0; it will be zero after 18 hours, 36 hours, 54 hours and 72 hours, So if we observer each 24 hours then the phase will not be zero again during our observation until after three days.

   True

   False

6. What is the range of pixel values inside the inner circle for this star? (Find the maximum and minimum values.

   		Pixel Values Minimum 1633 Maximum 31495
   		Pixel Values Minimum 16330 Maximum 31495
   		Pixel Values Minimum 16330 Maximum 17865

a stream of alpha particles moves with a velocity of 0.05m/s through a gate where a magnetic field is 1 Tesla (applied into page)

- o a o -

- o o -

- o o -

- -

o o o o o o

o o o o o o

o o o o o o

a= alpha particle

1.what is the magnitude and direction of the elcectric force on the particle

2 what is the magnitude and direction of magnetic force on particle

3 in what condtion would the particle move perpendicular to both the field and pass through the gate. find the magnitude of electric field

-----particle passed through gate and move in a magnetic field of 1 tesla perpendicular to the field

4 what kind of trajectory would it follow

5 what is the acceleration

6 .what would be the angular acceleration and angular velocity

7 .any perodic motion? if yes find the frequency

A rocket moves with a speed of 45 m / s. The rocket suddenly breaks into two parts of equal mass that fly at speeds v1 and v2. Obtain the magnitude of the velocity of each part in which the rocket broke.

Synchronous communication satellites are placed in a circular orbit that is 1.88 × 10⁸ m above the surface of the earth. What is the magnitude of the acceleration due to gravity at this distance?

The most mass of our Milky Way is contained in an inner region close to the core with radius R0. Because the mass outside this inner region is almost constant, the density distribution can be written as following (assume a flat Milky Way with height z0):

ρ(r) = p0, when r< or = to R0

0, when r >R0

(b) Derive the expected rotational velocity of the Milky Way v(r) at a radius r.
(c) Astronomical observations indicate that the rotational velocity follows a different behaviour:

Draw the expected and observed rotational velocity into the plot below:

(d) Scientists believe the reasons for the difference to be dark matter: Determine the rotational velocity due to dark matter vDM (r) from R0 and draw it into the plot above.
(e) Derive the dark matter mass MDM (r) enclosed in r and explain its distributed.
(f) Explain briefly three theories that provide explanations for dark matter.
(a) Derive an expression for the mass M (r) enclosed within the radius r.