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The half-life of radium-226 is 1620 years. How much of one gram of radium-226 will remain unchanged after four half-lives?

a) 0.125 g
b) 0.50 g
c) 0.0625 g
d) 0.25 g

Respuesta :

syed514
The correct answer is option C : 0.0625g of one gram of radium-226 will remain unchanged after four half-lives. 

Answer:

0.0625 g

Step-by-step explanation:

Given : The half-life of radium-226 is 1620 years.

Formula of half life:

[tex]P(t) =P_0(\frac{1}{2})^\frac{t}{1620}[/tex]

So. [tex]P_0[/tex] = initial amount

P(t)= mass of radioactive material at time interval (t)

1 half life = 1620 years

4 half lives = 4 * 1620

So, t = 4 * 1620

Substituting the values :

[tex]P(t) =1 (\frac{1}{2})^\frac{4\times 1620 }{1620}[/tex]

[tex]P(t) = (\frac{1}{2})^4[/tex]

[tex]P(t) = \frac{1}{16}[/tex]

[tex]P(t) =0.0625[/tex]

Hence  0.0625 g of one gram of radium-226 will remain unchanged after four half-lives

Option C is correct.

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