Decay X!

Classical Mechanics Level 3

There is a radioactive material, which initially 100 grams. After a period of decaying it remains x x grams.

Also, the period can express as

t = x 100 T 1 2 t=\frac{x}{100} T_{\frac{1}{2}}

Find the value of x x . Approximate to 1 decimal place.

  • T 1 2 T_{\frac{1}{2}} describes half life period of the material.

  • Mass will decay to zero as time goes infinity.


The answer is 64.1.

Kelvin Hong by Kelvin Hong , 21, Malaysia

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1 solution

Kelvin Hong
Aug 8, 2017

Using formula

N N 0 = ( 1 2 ) t T 1 2 \frac{N}{N_0}=(\frac{1}{2})^{\frac{t}{T_{\frac{1}{2}}}}

N N , N 0 N_0 and t t describe mass of material, initial mass of material and time.

Which leads to equation

x 100 = ( 1 2 ) x 100 \frac{x}{100}=(\frac{1}{2})^{\frac{x}{100}}

We can let n = x 100 n=\frac{x}{100} to simplified the equation:

n 1 n = 0.5 n^{\frac{1}{n}}=0.5

Using Newton approximation or Wolfram Alpha to solve this equation, to get

n = 0.641186 n=0.641186

So x = 100 n = 64.1 x=100n=\boxed{64.1}

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