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I need help with The half-­life of a radioisotope is four hours. If the initial mass of the isotope was 200 g, the mass remaining after 24 hours undecayed is

The half-­life of a radioisotope is four hours. If the initial mass of the isotope was 200 g, the mass remaining after 24 hours undecayed is

  • Option 1)

    1.042 g

  • Option 2)

    2.084 g

  • Option 3)

    3.125 g

  • Option 4)

    4.167 g.

 
Answers (1)
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As learnt in the 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}{4}

\frac{0.693}{4} = \frac{2.303}{24} log \frac{200}{x}

6 X 0.3010 = log \frac{200}{x}

log 64 = log \frac{200}{x}

64 = \frac{200}{x}

x= \frac{200}{64}=3.125 gm


Option 1)

1.042 g

This option is incorrect. 

Option 2)

2.084 g

This option is incorrect. 

Option 3)

3.125 g

This option is correct. 

Option 4)

4.167 g.

This option is incorrect. 

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