PHYS 202 Final Exam 5/6/11 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 = 6 grams; q₂ = -2 microCoul, m₂ = 13 grams). The first particle is 15 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?

4.0 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) Consider a carton-12 ion (singly charged with one electron missing so it has a positive charge) and its mass is 12 amu.

a) If the ion is accelerated through a potential difference of 120 volts, what will the speed of the ion be if it started from rest?

4.38 x 10⁴ m/s.

b) If the voltage is doubled, will the speed of the ion be increased: [by less than a factor of 2, by a factor of 2, by more than a factor of 2]?

Less than a factor of 2.

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.

d) Connect the three resistors in a circuit (make a circuit drawing) such that the effective resistance is between 4 W, and 8 W.

4) Consider a carbon-12 positive ion (see problem 2) moving up at a speed of 7 x 10³ m/s in a magnetic field of strength 0.0271 T directed East.

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

3.04 x 10^-17 Nt.

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

North.

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

1.51 x 10⁹ m/s² .

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

Change direction.

5) Consider a series LRC circuit with an oscillating voltage source of 110 volts (rms) at 60 Hz. The resistance is 25 ohms, the capacitance is 22 microFarads, and the inductance is 70 milliHenries.

a) What is the capacitive reactance (X_C) ?

120.6 W

b) What is the inductive reactance (X_L) ?

26.4 W

c) What is the impedance (Z) of the circuit?

97.4 W

d) what is the rms current through this circuit?

1.13 Amps

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 lens is used as a magnifying glass and has a focal length of 27 mm (2.7 cm).

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

10.26 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 27 mm, that is, specify n_glass, R1 and R2 and draw a picture of the lens.

FOR PROBLEMS 8 AND 8 USE THE FOLLOWING INFORMATION: A 35 mm camera (film size is 24 mm x 36 mm) uses a lens with a focal length of 120 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 30 mm). You take a picture of a newspaper located 75 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.]

8) a) What is the object distance?

75 m.

b) What is the image distance? (If the distance is close to the focal length, make sure you indicate whether the distance is a little more or less than the focal length.)

120.2 mm.

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

6.41 mm = 6.41 x 10^-6 m.

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

Upside down.

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

2.24 x 10^-5 rad = 1.28 x 10^-3 degrees.

b) What angle does the print size (4 mm on the paper) make when viewed from 55 meters away?

5.33 x 10^-5 rad = 3.1 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.

10) a) List two experiments that indicate light behaves as a wave and not as a particle:

(1)

(2)

b) List two experiments that indicate light behaves as a particle and not as a wave:

(1)

(2)

11) a) What is the energy of a photon given off by a hydrogen atom in going from the n=4 state to the n=1 state?

12.8 eV = 2.04 x 10^-18 Joules.

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

97.5 nanometers = 9.75 x 10^-8m.

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

UV.

12) Given that the work function of a certain metal is 3.3 eV.

a) What is the cut-off frequency for the photoelectric effect with this metal?

7.96 x 10¹⁴ Hz.

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

377 nm = 3.77 x 10^-7 m.

c) What is the stopping voltage required for ultraviolet light of wavelength 155 nm?

4.72 volts.

d) Will ultraviolet light of wavelength 233 nm be able to eject electrons from this metal?

Yes.

e) Will blue light be able to eject electrons from this metal?

No.

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

(The one stable isotope of ₄₁Nb is at a mass of 93.)

₉₄Pu²⁴⁰ goes to ₉₂X²³⁶ + alpha + energy

₄₁Nb⁹⁷ goes to ₄₂ X⁹⁷ + _-1b⁰ + anti ₀n⁰ .

₄₁Nb⁹⁰ goes to ₄₀ X⁹⁰ + ₊₁b⁰ + ₀n⁰ .

14) Given that the half life of ₄₁Nb⁹⁷ is 72 minutes.

a) What is the decay constant for this isotope?

9.63 x 10^-3/min = 1.60 x 10^-4/second

b) How many atoms of Nb⁹⁷ are there in 1 gram?

6.19 x 10²¹ .

c) What is the activity of 1 gram of Nb⁹⁷ in dis/sec and in curies?

9.92 x 10¹⁷ Bq. and 2.68 x 10⁷ Curies

d) What will the activity of this one gram after 2 days (in dis/sec)?

9.02 x 10⁵ Bq.

15) C¹⁴ has a half life of 5,730 years, and the ratio of C¹⁴ to C¹² is 1.3 x 10^{-12 .}

a) What is the decay constant for C¹⁴?

1.21 x 10^-4/yr = 3.84 x 10^-12 /sec.

b) How many atoms of C¹⁴ are there in 4 grams of carbon, assuming the ratio given above?

2.61 x 10¹¹ .

c) What is the present activity of 1 gram of C¹⁴ taken from a modern “bone” (this assumes the present ratio of C¹⁴ to C¹²)?

in dis/sec? 1.00 Bq. In Curies ? 27 pCi = 2.7 x 10^-11 Curies.

d) Assuming the ratio of C¹⁴ to C¹² in the atmosphere has remained the same, what should the age of a bone be if 4 grams of carbon taken from the bone have an activity of 0.18 counts/sec ?

14,176 years.

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