Maths Question???

Question

Radio-isotopes of different elements have different half-lives. Magnesium-27 has a half-life of 9.45 minutes. What is the decay constant for Magnesium-27? Round to five decimal places.

I don't get this question...can any1 help plz???

Answer 1

Here's the general set up for any half-life problem:

.5 = e ^ -kt where k is the decay constant(notice the negative in front).

So what you want to do in this case is put 9.45 in for t, and then solve for k.

Answer 2

Notation:
....................................................
T1/2 = half life
lambda = "decay constant
ln(2) = 0.693147..
....................................................

A = A0 * 2^(-t/(T1/2)) = A0*e^(-.693*t/(T1/2))
= A0*e^(-lambda * t)

from this we can derive:
T1/2 = .693/lambda
lambda = .693 / (T1/2)

so in this case,
lambda = 0.693147 / 9.45 = 0.073348907....


"0.07335" is your answer, tho I want to point out that it's a odd to strive for "5 decimal places" when you start out with a "2-decimal place" data-item of "9.45"



0.07335 ... when you're dealing with "t" in minutes


eg, after one minute:
A = A0 * e^(-0.07335 * t) = A0 * 0.92928

meaning that for every 1000 atoms you started with there are 929 left after one minute (due to radioactive decay)


the web-site I list is pretty helpful

Answer 3

e^-kt = m1/m0
-9.45k = ln(0.5)
k = -0.07335/min.