I understand that t (0.5) can be derived from the equation that relates N0,Nt and gamma. thing is i always get confused with it, and have trouble using the derived equation in questions. In the solution to question 2 at the free practice at testprep-online states that using the equation to solve the question demands elaborate computation, and thus a tricky solution is offered instead (I call it tricky since it reminds me of those shortcuts that are always offered in SAT and ACT, which I never figured out). I just wanna get the elaborate calculation for that question, just to get a grip of the concept and then think about tricking it out. Can anyone help?
the half life equation
- Thread starter I say mm
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so half life is where N= N0/2
given the equation: N(t)= (N0)e^(-t*y) where N0 is the initial amount and y is gamma, the time constant
at half life, N(t)= 1/2*N0= (N0)e^(-t*y)
canceling out N0, 1/2= e^(-t*y)
take the natural log of both sides:
ln(1/2)= -t*y
t= -1*(ln(1/2))/y
and this is always true for an half life; thus half life depends exclusively on the time constant gamma
given the equation: N(t)= (N0)e^(-t*y) where N0 is the initial amount and y is gamma, the time constant
at half life, N(t)= 1/2*N0= (N0)e^(-t*y)
canceling out N0, 1/2= e^(-t*y)
take the natural log of both sides:
ln(1/2)= -t*y
t= -1*(ln(1/2))/y
and this is always true for an half life; thus half life depends exclusively on the time constant gamma
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No, just understand the concepts.
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I've gotten away with my ability to divide and multiply by 2, and my comfort with scientific notation... 🙂
it really is that simple usually.
it really is that simple usually.
