Problem Set 4 Kleiban (Spring 2013)
1. Molybdenum has a workfunction of 4.2 eV. (a) Find the cutoff wavelength and the threshold frequency for the photoelectric effect. (b) Calculate the stopping potential if the incident light has a wave- length of 180 nm.
2. A photon of initial energy 0.1 MeV undergoes Comptom scattering at an angle 0f 60o. Find (a) the energy of the scattered photon (b) the recoil energy of the electron (c) the scattering angle of the electron Remember… these electrons have relativistic velocities.
3. A 0.0016 nm photon scatters from a free electron. For what (photon) scattering angle will the recoiling electron and scattered photon have the same kinetic energy?
4. A neutron beam with a speed of 0.6 m/s is directed through a double slit with 0.75mm separation. An array of detectors is placed 12m from the slits. (a) What is the de Broglie wavelength of the neutrons? (b) How far off axis is the first zero intensity point on the detector array?
5. An electron has a wavefunction
√ 2 L
sin ( 2πx L
Find the probability of finding the electron between x=0 and x=L/4.
1) A football team is in a position to kick a field goal to win a game. The ball is placed 36 m (approximately 39 yards) from the goalposts. The kicker kicks the ball with a resultant velocity of 20 m/s at an angle of 33°.
List your knowns: (2 pts)
What was the initial horizontal velocity? (2 pts)
What was the initial vertical velocity? (2 pts)
How long was the ball in the air (total flight time)? (4 pts)
What was the horizontal distance traveled? Did they win? (4 pts)
Calculate the following quantities for the diagram shown below: (16 points total)
a. The angular velocity at the hip over each time interval (6 points)
b. The angular velocity at the knee over each time interval (6 points)
Would it be meaningful information to calculate the average angular velocities at the hip and knee for the movement shown? Provide a rationale for your answer. (4 points)
A soccer ball is kicked from the playing field. If the ball is in the air for 2.2 s (total flight time), what is the maximum height achieved? (4 points) (neglect air resistance)
Two cyclists B1 and B2) are racing at exactly the same velocity (say, 12 m/s) and come to a curve in the road (point A). At this point they are tied. Throughout the first half of the curve (points A-C), it appears that the cyclist in the outside lane (B2) remains tied with the cyclist in the inside lane (B1). Assume that the cyclist in the inside lane (B1) maintains a constant velocity. Using terms such as “constant”, “zero”, “same”, “increase”, “decrease”, “positive”, “negative” etc. answer the following questions:
a) What are the differences (if any) between the linear distances traveled by the cyclists between points A and C. List the equation that explains this. (4 points)
b) What are the differences (if any) between the tangential (linear) velocities of the cyclists at points A and C. List the equation that explains this. (4 points)
c) What are the differences (if any) between the tangential (linear) accelerations of the cyclists
between points A and C. List the equation that explains this. (4 points)
d) What is the difference (if any) between the radial acceleration of B1 at points A and C. What is the difference (if any) between the radial acceleration of B2 at points A and C. List the equation that explains this. (4 points)