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### Course: AP®︎/College Physics 2>Unit 8

Lesson 3: Nuclear physics

# More exponential decay examples

A few more examples of exponential decay. Practice calculating k from half-life, and calculating initial mass.  Created by Sal Khan.

## Want to join the conversation?

• Sal says that after one half life, you could expect 50% of the substance to decay. Since the particles have only a 50% chance of decaying, Is it possible for the substance to not decay at all after one half life?

(1 vote)
• possible: yes
likely: no
If you have lets say 131 grams of Iodine(131) which has a half-life of 8 days and you let it sit for 8 days, the probability for "no atom of Iodine(131) has decayed" would be the same as if you throw 6*10^23 coins and all of them would show "heads".
• 10 to the power of X

i.e log (100) = 2
Therefore 10 ^ 2 = 100 which is true :)

As a more general rule Log a ( b ) = Log ( a ^ b )
In chemistry log base 10 is used almost all the time so: a will always = 10

edit: Just saw that in this video Log base e is used and not log base 10.

i.e the inverse of Log base 10 ( b ) = 10 ^ b
and the inverse of Log base e ( b ) = e ^ b

Hope that helps :)
• this question might seem a little off topic but if atoms can decay is there something opposite to that?
• No. Nuclei don't spontaneously add protons or neutrons.
You might call electron capture the opposite of beta decay.
In beta decay, a nucleus spontaneously emits an electron. In electron capture, a nucleus captures an inner electron.
However, the same nucleus doesn't undergo both processes.
• Can you show me how to calculate a 1/2 life using disentegrations per minute. For example, I start with a compound that is 9.7 x 10^5 dpm, then several days later I end up with 2.2dpm, how do I figure out the half life?
• Disintegrations per minute are handled the same way as number of atoms. DPM are considered an activity A(t), so instead of the equation N(t)=No*exp(-kt) you have A(t)=Ao*exp(-kt). From the talk, he mentions that half-life = ln(2)/k, so use the above equation for A(t) above, solve for k, and then convert to half-life.
• Does anyone know of somewhere I can practice problems like these?
• You can Google practice problems and PDFs usually pop up with the answers at the bottom for practice, that's how I practiced chemistry problems. Good luck!
• What doe kt stand for?
• I'm having a hard time understanding what K is. Help!
• Can I use the formula N = N_0 (0.5) ^ (t / n), where N is the final amount, N_0 is the starting amount, t is the time and n is the half life to solve these problems as well?
• I have a question about the time units. Do I always have to convert any unit time given to years? Or can I use another unit as well? Thank you.
(1 vote)
• The time units will depend on the process being modeled, but must be used consistently.

For example, if you determined k using t in seconds, then the half-life would also be in seconds.

Similarly, if you are given a k then you need to know what time units were used to derive that value.

Does that help?