PHYS 202 Final Exam 5/11/09 Dr. Holmes NAME

DO ALL THE PROBLEMS. THE WORTH OF EACH PROBLEM IS MARKED NEXT TO THE PROBLEM. SHOW YOUR WORK FOR PARTIAL CREDIT.

1) Consider two charged particles (q₁ = -5 microCoul, m₁ = 16 grams; q₂ = +3 microCoul, m₂ = 33 grams). The first particle is 25 cm to the West of the second one.

a) What is the magnitude and direction of the electric FORCE on the first particle due to the presence of the second particle?

2.16 Nt, East

b) Is the magnitude of the force on the 2^nd particle due to the 1^st particle bigger, the same as, or smaller than the force on the 1^st particle due to the 2^nd particle?

Same.

c) Is the direction of the force on the 1^st particle due to the 2^nd particle the same or opposite that of the force on the 2^nd particle due to the 1^st particle?

Opposite.

d) Is the magnitude of the acceleration of the 2^nd particle due to the presence of the 1^st particle bigger, the same as, or smaller than the acceleration of the 1^st particle due to the 2^nd particle? (Assume there are no other forces acting on the two particles).

Smaller.

2) An electron is initially at rest and at a location where the potential is +50 volts.

a) Will the electron tend to go to a position where the voltage is higher or lower?

Higher.

b) What will be the speed of the electron at a new position that is different by 100 volts (i.e., either -50 volts or +150 volts, based on your answer to the first part)?

5.93 x 10⁶ m/s.

3) Consider three resistors: R₁ = 4 W, R₂ = 8 W, and R₃ = 12 W.

a) Connect the three resistors in a circuit (make a circuit drawing) such that the effective resistance is the smallest it can be:

b) Are the three resistors above connected in series, parallel, or some other combination?

Parallel.

c) What is the effective resistance of this circuit that has the smallest effective resistance using these three resistors?

2.18 W.

4) Consider a proton moving East at a speed of 4 x 10³ m/s in a magnetic field of strength 0.0081 T directed down.

a) What is the magnitude of the magnetic force on the proton?

5.18 x 10^-18 Nt.

b) What is the direction of the magnetic force on the electron?

North.

c) What is the magnitude of the acceleration of the proton due to this force?

3.10 x 10⁹ m/s² .

d) Will this magnetic force cause the proton to speed up, slow down, or change direction?

Change direction.

5) DESIGN an electric generator that will provide 220 volts rms: To do this, draw a picture and then specify the values of all the relevant parameters:

6) In each of the four diagrams below, indicate on the A circuit the direction of the induced current in circuit A due to the situation described (if no current, then write the word NONE on circuit A):

a) the external magnetic field directed UP through circuit A is DECREASING in strength:

b) the South pole of the bar magnet is moved away from the solenoid (cylinder wrapped with wire) in circuit A:

c) the bar is moving to the right:

d) the switch in circuit B is being CLOSED (it was open):

7) A light ray coming from air (n_air=1.00) toward glass (n_glass = 1.67) strikes the air/glass surface at an angle of 69^o with respect to the SURFACE.

a) What is the angle of REFLECTION as measured from the SURFACE?

69^o.

b) What is the angle of REFLECTION as measured from the NORMAL?

21^o.

c) What is the angle of the light TRANSMITTED into the glass as measured from the NORMAL? (If totally reflected, write TIR.)

12.4^o.

d) Is it possible for the ray of light in the air to be totally reflected from the glass?

No.

8) A lens is used as a magnifying glass and has a focal length of 12 mm.

a) What is the magnifying power of the lens when used correctly?

21.8 X .

b) Draw a diagram showing the object, the lens, the focal length of the lens, the eye, and the image.

c) Design a lens that has the above focal length of 12 mm, that is, specify n_glass, R₁ and R₂ and draw a picture of the lens:

FOR PROBLEMS 9 AND 10 USE THE FOLLOWING INFORMATION: A 35 mm camera (film size is 24 mm x 36 mm) uses a lens with a focal length of 135 mm and the f-stop setting is 4 (which means the diameter of the opening to the lens is 1/4 the focal length or 33.75 mm). You take a picture of a newspaper located 80 meters away. The size of the print on the page is 4 mm. For purposes of calculation assume that the wavelength of the light is one in the middle of the visible spectrum. [If you do not know what wavelength this is, you may ask and I will give it to you but you will be marked down one point.]

9) a) What is the object distance?

80 m.

b) What is the image distance?

135.2 mm.

c) Given that the print size on the paper is 4 mm in height, what is the image height on the film?

6.76 mm.

d) Is the image upside down or right-side-up?

Upside down.

10) a) What is the smallest angle that this camera can resolve based on the Rayleigh criterion?

1.99 x 10^-5 rad = 1.14 x 10^-3 degrees.

b) What angle does the print size (4 mm on the paper) make when viewed from 80 meters away?

5 x 10^-5 rad = 2.86 x 10^-3 degrees.

c) Assuming the camera has quality lenses and a fine grain film, can the picture the camera takes be enlarged big enough and clearly enough so that you can read what the newspaper said (definitely, just barely, not quite, definitely not) ?

Just barely.

11) a) Given that the work function of aluminum is 4.2 eV, what is the cut-off frequency for the photoelectric effect with aluminum?

1.01 x 10¹⁵ Hz.

b) What wavelength is associated with this cut-off frequency?

296 nm.

 c) What is the stopping voltage required for ultraviolet light of wavelength 120 nm?

6.16 Volts.

12) a) What is the energy of a photon given off by a hydrogen atom in going from the n=4 state to the n=3 state?

0.66 eV = 1.06 x 10^-19 Joules.

b) What is the wavelength of light from this transition?

1.88 micrometers = 1.88 x 10^-6m.

c) What type (or if visible, what color) is this photon?

Infrared.

13) a) What is the speed of an electron accelerated through 70 volts?

4.96 x 10⁶ m/s.

b) What is the momentum of this electron (at the above speed)?

4.51 x 10^-24 kg*m/s

c) What is the wavelength of this electron (at the above momentum)?

1.47 x 10^-10 m = 0.147 nm.

d) What is the wavelength of a photon that has an energy of 70 eV ?

1.78 x 10^-8 m = 17.8 nm.

14) Fill in the missing particle(s): (use X for the element name if you do not know it)

(There is one stable isotopes of ₅₉Pr at a mass of 141.)

₉₄Pu²³⁹ goes to ₉₂X²³⁵ + alpha + energy

₅₉Pr¹⁴⁰ goes to ₅₈ X¹⁴⁰ + ₊₁b⁰ + ₀n⁰ .

₅₉Pr¹⁴² goes to ₆₀ X¹⁴² + _-1b⁰ + anti- ₀n⁰ .

15) a) Given that the half life of ₅₉Pr¹⁴² is 19 hours, what is the decay constant for this isotope?

1.01 x 10^-5 /sec.

b) How many atoms of Pr¹⁴² are there in 1 gram?

4.24 x 10²¹ .

c) What is the activity of 1 gram of Pr¹⁴²

in dis/sec? 4.3 x 10¹⁶ Bq. In Curies ? 1.16 x 10⁶ Ci.

d) What will be the activity of this one gram after 1 week in dis/sec ?

9.36 x 10¹³ Bq.

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