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Help me please, The half­-life of a radioactive isotope is three hours. If the initial mass of the iosotope were 256 g, the mass of it remaining undecayed after 18 hours would be

The half­-life of a radioactive isotope is three hours. If the initial mass of the iosotope were 256 g, the mass of it remaining undecayed after 18 hours would be

  • Option 1)

    4.0 g

  • Option 2)

    8.0 g

  • Option 3)

    12.0 g

  • Option 4)

    16.0 g.

 
Answers (1)
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As we learnt in concept

First Order Reaction -

The rate of the reaction is proportional to the first power of the concentration of the reaction

- wherein

Formula:

R    \rightarrow        P

a                 0

a-x             x

rate[r]=K[R]^{1}

\frac{-d(a-x)}{dt}=K(a-x)

\frac{-dx}{dt}=K(a-x)  [differentiate rate law]

ln \:[\frac{a}{a-x}]=kt \:(Integrated rate law)

Unit of k=sec^{-1}

t_\frac{1}{2}=\frac{0.693}{k}

 

 

 K = \frac{0.693}{3}\\ \frac{0.6933}{3} = \frac{2.303}{18} log \frac{256}{x}

\frac{6 X 0.693}{2.303} = 6 X \log _{2} = \log \frac{256}{x}

X = 4 gm 


Option 1)

4.0 g

This option is correct. 

Option 2)

8.0 g

This option is incorrect. 

Option 3)

12.0 g

This option is incorrect. 

Option 4)

16.0 g.

This option is incorrect. 

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