Question

Radium has a half-life of 1,620 years. In how many years will a 1 kg sample of radium decay and reduce to 0.125 kg of radium?

1,620 years

3,240 years

4,860 years

6,480 years

Answer 1

Please help me :(

Answer 2

hint: 0.125 = 1/8

Answer 3

The formula for half-life is:\[\frac{1}{2} N_0=N_0 e^{kt}\]Simplified that becomes:
\[\frac{1}{2}=e^{kt}\]
First you need to solve for k. There are two ways you can do this for a half-life problem. The simplest is if you know the formula:\[Half-life=1620=\frac{-ln(2)}{k}\]\[k=\frac{-ln(2)}{1620)}=-4.278686x10^{-4}\]
The second method is just mathematically solving the half-life formula for k:
\[\frac{1}{2}=e^{kt}\]\[\frac{1}{2}=e^{k(1620)}\]\[ln(\frac{1}{2}) =k(1620)\]\[k=\frac{ln(\frac{1}{2})}{1620}\]\[k=-4.278686x10^{-4}\]

Now that you know k you can solve the equation for t:\[0.125kg=(1kg)(e^{(-4.278686x10^{-4})t)}\]\[t=\frac{ln(0.125)}{-4.278686x10^{-4}}=4860\space years\]

Answer 4

thank you , i thought it was c :)

Answer 5

= 1620*3.

Answer 6

do you know this question?
According to the theory of evolution, amphibians evolved from ancient fish. Which of these would best validate the theory?

record of history of a place

a study published by a research scholar

record of temperature changes of a place

a study crediting the theory by many scientists

Answer 7

None of those are all that great, but historical data is probably best, followed by the study with numerous citations.

The best validation for a theory is its predictive power and resistance to being falsified.

Answer 8

@CliffSedge: Was there a simpler method for the first question? I've always done those solving for k.

Answer 9

Yes. If there is 0.125kg remaining of the original 1kg, then there is 1/8 remaining. 1/8 = (1/2)^3

Answer 10

Ah...I didn't see that. Thanks :)

Answer 11

For half-life, you can start with final = original*(0.5)^n, n= number of times it was cut in half, so multiply that by the half-life time period.

Answer 12

correct^ its actually pretty simple after you learn it :)

Answer 13

I've always done it using the way I posted which is only slightly more work once you're familiar with it...habit I guess.

Answer 14

Still, it's important to know the general exponential function equation for different scenarios.

Answer 15

@Shane_B it's a tool that always works, but like the quadratic formula, sometimes it's overkill. Would you use QF for x^2-4=0?

Answer 16

Nope :)

Answer 17

My method is to not memorize formulas, but to always (if I can) derive the one I need based on the situation. If I can't derive it myself, then I go looking for the general formula.