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GR0177 #66
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Alternate Solutions |
travis.nicholson
2006-10-23 01:04:11 | The crux of this problem is that the total decay rate of the sample is equal to the sum of the decay rates through each decay channel.
N = -k_total*N)
Since the half life, , is given by /\tau)
Therefore,  = 14.4min) |  |
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Comments |
anmuhich
2009-03-16 13:11:24 | You can also figure out the answer just by looking at the answers and thinking about rates of decay. If you only had gamma emission half the sample would decay in 24 minutes, so A is out. It's going to be less than 24 minutes because you also have beta emission, so B is out. Since the beta emission is slower than the gamma you know that the half life will be longer than half of the gamma emission. This eliminates E. 20.8 minutes is too close to 24 for that to be the half life of just gamma emissions, especially when you also have the beta emissions, so the answer must be 14.4 D. |  | carl_the_sagan
2008-11-07 20:29:54 | This is just a glorified rate problem like you see on the general GRE. Gamma gets you half the work done in 24 minutes, Beta gets you half the work done in 36 minutes. Working together you have:
 = 14.4
Granted they are really decays, but the same idea applies, and you didn't have to mess with logs and any other nonsense.
giga17
2010-08-11 02:19:21 |
Agree with this. In fact, it is essentially related to the concept of reduced mass.
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| | chrisfizzix
2008-09-23 13:38:26 | Here's how I solved this problem, which is the same method except a slightly different form.
We have a decay process with two different channels; the probability that the sample has not decayed at time  from the decay process  is  , where is the half-life. The total probability then is  } ) . Then we can find the half-life  .
When I was taking this test as practice, I didn't remember anything about decay processes except the simple exponential decay rule, and that probabilities multiply. | | Blake7
2007-09-21 20:56:10 | Is it just me, or did ETS throw easier numbers at us to work with in 0177?
Come on, divide 24(36)/60 !?!? 14.4 about falls out!
(Oooooh, pardon the pun! Get it? "falls out")
irishroogie
2007-10-02 13:39:56 |
Did you know that an overusage (and particularly a delight in the usage) of puns is a sign of mental illness. Totally random fact but I heard it on the radio and then checked out the literature on it... It's true!!!
(I am not implying anything here Blake7 but be careful :) )
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| | travis.nicholson
2006-10-23 01:04:11 | The crux of this problem is that the total decay rate of the sample is equal to the sum of the decay rates through each decay channel.
Since the half life,, is given by
Therefore, | | herrphysik
2006-09-28 00:10:45 | Everywhere you have }) you should have }) . You're forgetting the minus sign, and }=ln{(2)}) . Plus, remember the simple half-life formula is just }/\lambda) . This error doesn't change the answer since it all cancels out, but it adds to the confusion. Also, to answer ee7klt,  the number of radioactive particles in the sample. |  | ee7klt
2005-11-11 04:18:09 | Hi,
How did the  and  factor out in to  (what is ?) in the second to last step?
cheers. | |
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