Determine the number of combined states, in the form of total |s m s >, for the combination of four spin ½ particles.

Do NOT determine the coefficients in the composite states.

Hint: make two combinations of spin - ½ particles, one for spins 1 and 2, and one for spins 3 and 4, and combine those

A small conducting spherical shell with inner radius a and outer radius b is concentric with a larger conducting spherical shell with inner radius c and outer radius d. The inner shell has a total charge of -2q and the outer shell has a total charge of +4q.

Select True or False for the following statements.

The total charge on the inner surface of the small shell is zero.
True False  The total charge on the inner surface of the large shell is zero.
True False  The electric field in the region r < a is zero.
True False  The electric field in the region r > d is zero.
True False  The total charge on the outer surface of the large shell is +2q.
True False  The electric field in the region c < r < d is zero.
True False  The total charge on the outer surface of the small shell is -6q.

Smarty McGuy intends to charge the parallel plate capacitor inside his intergalactic Ford Pinto (built by Doc Dre) with a lightning strike of 26x10³ amps. Doc Dre's capacitor specifications are listed below:

The distance between the capacitor plates is 5 microns

The surface area of the capacitor plates is 3,844 cm²

There is a dielectric between the capacitor plates

What is the minimum dielectric constant of the material between the plates needed to store all the charge from the lightning assuming that the lightning strike lasts for 6x10^-6 seconds and provides 1.21 Gigawatts of power? Assume the dielectric doesn't reach its breakdown voltage.

(a) Name 4 major components of a Gamma camera. Briefly explain the function of each component.
Also, describe the advantages and disadvantages of using “thin” scintillating crystal.

(b) In an experiment with 51.80 MBq 99mTc, 5.88×105 counts are measured in 2 minutes. According to the manufacturer the sensitivity is 202 cnts/(min⋅μCi) (American manufacturers still use Ci instead of Bq, 1μCi = 37 kBq). What is the difference between the sensitivity of the measurement and the factory specification?

(c) in a NM scan, we use a specific contrast agent with half-life of 2h and emitted gamma radiation with wavelength of the 8.79x0-12 m. We image the patient immediately after the injection and the scan takes 20 minutes. Injecting 1 mCi, the acquired NM images have signal-to-noise ratio of 40. Calculate the SNR if we inject the patient with 3 mCi and scan him for 60 minutes.

Explain two reasons behind the commercial failure of Low Earth Orbit satellite mobile communications companies (such as Iridium).

An object with total mass m_total = 14.8 kg is sitting at rest when it explodes into three pieces. One piece with mass m₁ = 4.8 kg moves up and to the left at an angle of θ₁ = 22° above the –x axis with a speed of v₁ = 27.6 m/s. A second piece with mass m₂ = 5.1 kg moves down and to the right an angle of θ₂ = 27° to the right of the -y axis at a speed of v₂ = 20.5 m/s.

What is the x-component of the velocity of the third piece?

What is the y-component of the velocity of the third piece?

What is the magnitude of the velocity of the center of mass of the pieces after the collision?

Calculate the increase in kinetic energy of the pieces during the explosion？

A gas of nitrogen molecules is at a temperature of 1000K. In this case molecule has 3 translational, 2 rotational, and 2 vibrational degrees of freedom per molecule, i.e. a total of 7.

1.9. [1pt] Assuming the cycle operates as an engine, calculate the engine efficiency.

ANSWER

1.10. [1pt] If you are to build the most efficient engine using the highest and the lowest temperatures available from #9 how would the cycle look like on a PV-diagram [you need to indicate both cycles]

ANSWER

1.11 [1pt] What is the efficiency of the most efficient cycle in 1.10?

ANSWER