In-class group activity 15:  Alpha decay

Use an on-line simulation from the University of Colorado PhET group to stydy alpha decay

Explore the interface!

• You can Pause the simulation and then use Step to incrementally analyze.
• After the Polonium nucleus decays to Lead, click Reset to start over with a new Polonium nucleus.

Click the ‘Single Atom’ tab.

• Watch the Polonium-211 nucleus until it decays.  Click ‘Reset Nucleus’ and watch it again.  Repeat this at least 10 more times.

• Inspect the Decay Time Chart on the top of the screen.  It displays the decay times of all the nuclei you observed.  Do you observe a pattern?  Can you predict the decay time for the next nucleus?

Question 1
The half-life of the Polonium-211 nucleus is approximately 500 ms.  The nucleus decays by emitting an alpha particle.  How does this alpha particle make it out of the nucleus.  (Watch what happens in the bottom-half of the display in "Single Atom" mode.)

(a) A photon supplies the energy to lift it over a potential barrier. This is similar to the photoelectric effect, where a photon supplies the energy to an electron to free it from a metal.
(b) Collisions with other nucleons supply the energy to lift the alpha particle over a potential barrier.
(c) The alpha particle just tunnels through the barrier. The tunneling probability is relatively high, because the barrier is not much higher than the total energy of the alpha particle inside the nucleus.

Question 2
After the Polonium-211 nucleus has decayed, a lead-207 nucleus is left behind.  Why does lead-207 not decay by emitting an alpha particle?

(a) Lead-207 does not have enough nucleons to decay.
(b) Even though alpha particles penetrate into the potential barrier, they cannot tunnel through the barrier, because they cannot emerge on the other side with positive kinetic energy. In lead-207, the potential barrier for alpha particles is infinitely thick.
(c) In lead-207, the potential barrier for alpha particles is infinitely high.
(d) Lead 207 does decay by emitting an alpha particle, it just has a half-life longer than a few seconds, and so we do not see the decay in the simulation.

Question 3
In "Single Atom" mode switch to a custom nucleus.  What can you do in the bottom-half of the display to build a nucleus with a half-life of a billion years?

(a) Lower the total energy of the alpha particle so that it is barely bigger than the potential energy at infinity and raise the height of the barrier.
(b) Make the total energy and the barrier height equal to each other.
(c) Lower the total energy of the alpha particle so that it is less than the potential energy at infinity.
(d) It is impossible to achieve this in this simulation.

Click the ‘Multiple Atoms’ tab.
Quickly empty the Bucket of Polonium by rapidly clicking the ‘Add 10’ button until the bucket is empty.

• Observe the decay of the nuclei and inspect the Decay Time Chart on the top of the screen.

• Click ‘Reset All Nuclei’.  Do you observe the same pattern on the Decay Time Chart as in your previous trial?   Repeat this experiment a few times to be sure of your answer.  Describe any similarities and/or differences in pattern on the Decay Time Chart.

Question 4
The half-life of the Polonium-211 nucleus is approximately 500 ms.  What do you observe in "Multiple Atoms" mode?

(a) Exactly 50% of the nuclei decay in a time interval shorter or equal to 500 ms.
(b) More than 50% of the nuclei may decay in a time interval shorter or equal to 500 ms, but some may live longer than 2 s.
(c) More than 50% of the nuclei always live longer than 500 ms, but some decay immediately.
(d) All nuclei always decay in a time interval less than 1 s.

Question 5
If you would start out with ~8000 Polonium-211 nuclei at t = 0, approximately how many Polonium-211 nuclei would you have left at t = 2 s?

(a) zero
(b) 2000
(c) 4000
(d) 800
(e) 250
(f) 500