Chemistry I Extra Credit Assignment: “Fun With DeBroglie”

Show all work in answering these questions. Answer on a separate paper. These questions must be answered correctly and verified to receive credit. All work must be shown. You may need to ask further questions to complete it. Because of the challenging nature of this assignment, it is worth 10 extra credit homework points.

Plank's equation assumes that light, which we consider to be a wave, can be modeled as a particle with the energy of a particle of light (a “photon”) given by E = h. In 1924, Louis DeBroglie, a graduate student, proposed that if a light wave could be modeled as a particle, then perhaps particles could be modeled as waves. The wavelength of a particle with a mass = m and velocity = v can be calculated by theequation:

λ =h

mvwhere m = mass in kilograms and v = velocity in

meters/second. This wavelength is known as the “DeBroglie Wavelength”

Perform the following calculations. Show your work and show that the

units cancel to the appropriate unit for your answer. (1J=1kg⋅m2

s2 )1. Calculate the DeBroglie wavelength for:

a. A 2000 kg truck traveling 60 km/hour. You will need to convert the velocity to meters/second.

b. A 0.001 kg ping pong ball traveling at a speed of 100 m/s.

c. An electron traveling at a speed of 30 m/s. The mass of an electron is 9.11 x 10-31 kg

2. Using your results from question #1, rank the truck, ping pong ball and electron by energy from least to greatest. Explain how you determined the ranking.

Extra Challenge Problems - DeBroglie Wavelength 1 DeBroglie.odt

3. According to Einstein's theory of special relativity, the mass of a particle is affected by its velocity. This effect is very small at the velocities that we normally experience, but is important for objects whose velocity approaches the speed of light. In fact, an object with amass greater than 0 will have an infinite mass if it could travel at the speed of light! Because mass changes with the velocity of the

particle, we cannot use the formula for kinetic energy (E=12

mv2) to

calculate the energy of high velocity particles. We can compare energies by looking at their wavelength however. For objects moving at very high velocities, the formula for the DeBroglie Wavelength becomes:

λ =h

mv⋅√1−

v2

c2where c = the speed of light = 3.00 x 108 m/s.

Explain why you can use the simpler form of the DeBroglie equation (on the front page of this handout) for objects traveling at speeds much lower than the speed of light, but you must use the above equation when objects are traveling at speeds close to the speed of light. Hint: What happens to the value of the square root factor when v is a very small value such as 30 m/s?

4. An alpha particle is a high energy particle that is emitted by a nucleus of an atom during radioactive decay. It is made of 2 protons and 2 neutrons with a +2 charge. The mass of a proton or neutron is 1.67 x 10-24 g. Alpha particles travel at typical speeds of 15000 km/s.

a. Calculate the mass in grams of an alpha particle by adding the masses of the protons and neutrons in it.

b. Calculate the DeBroglie wavelength of an alpha particle traveling at a speed of 15000 km/s.

c. Gamma radiation, which is also emitted during radioactive decay has a wavelength of about 10-12 m. Which has greater energy, the alpha particle described above or Gamma radiation? Explain your reasoning.

Extra Challenge Problems - DeBroglie Wavelength 2 DeBroglie.odt

Solutions to: “Fun with DeBroglie”

1. a. 2 x 10-38 m b. 7 x 10-33 m c. 2 x 10-5 m

2. electron < ping pong ball < truck Explanations may vary.

3. Answers may vary

4. a. 6.68 x 10-27 kg b. 6.6 x 10-15 m c. answers may vary

Extra Challenge Problems - DeBroglie Wavelength 3 DeBroglie.odt