exponential growth and decay (1 Viewer)

[luvotomy]

can someone please help me with the question below:

The half-life of radium is 1600 years.
Find the percentage of radium that will be decayed after 500 years?

 

[shaon0]

can someone please help me with the question below:

The half-life of radium is 1600 years.
Find the percentage of radium that will be decayed after 500 years?

16.7%...lol..i guessed my answer

 

[lyounamu]

can someone please help me with the question below:

The half-life of radium is 1600 years.
Find the percentage of radium that will be decayed after 500 years?

The rate at which the radium decays is proportional to its amount. Therefore, the equaion of the radium is given at any given time (T) is given by:

R = Rie^(-kt) where Ri is the initial amount of radium.
When t = 1600, R =1/2 Ri
1/2 Ri = Rie^(-1600k)
1/2 = e^-(1600k)
-1600k = ln 1/2
k = 0.00043321...

Therefore, R = Rie^(-0.00043321... x t)
When t = 500, R = Rie^(-0.00043321... x 500)
= 0.80524516... x Ri
Therefore, R = 81% Ri

Therefore, approximately 81% remains after 500 years. (i.e. 19% is decayed)

 

[lyounamu]

16.7%...lol..i guessed my answer

It's pretty close considering that your answer was a guess.

 

[shaon0]

It's pretty close considering that your answer was a guess.

Not really a guess...it was:
(e^5/e^16)*10 000

 

[Forbidden.]

Not really a guess...it was:
(e^5/e^16)*10 000

That must be the equivalent of trapezoidal rule to integration.
LOL.

 

[lyounamu]

That must be the equivalent of trapezoidal rule to integration.
LOL.

???

 

[Forbidden.]

???

I'm saying he used a more rough method using estimation rather than use accurate methods of solving the question.

 

[3unitz]

T_1/2 = ln 2 / k
1600 = ln 2 / k
k = ln 2 / 1600

N = 100 e^-k500
~ 80.52%

 

[lyounamu]

I'm saying he used a more rough method using estimation rather than use accurate methods of solving the question.

Oh, ok.

 

[lolokay]

(1/2)^n = 1600n
n = 5/16
amount left: (1/2)^(5/16)
= 0.805
amount decayed = 0.195