Question

You start out with 800 moles of a radioactive substance. After 24 hours, 100 moles remain. What is the half-life of the substance in hours?
Question 1 options:

6 hours


12 hours


4 hours


8 hours

Answer 1

The half life of the substance is 8 hours , Option D is the correct answer.

What is Half Life ?

Half-life is the time required by an unstable element  to reduce to half of its initial value.

The term is commonly used in nuclear physics.

The formula is

$\rm N(t) = \; N_{0} \;(\dfrac{1}{2} )^{\frac{t}{t_{1/2} } }$

N(t)     =    quantity of the substance remaining

N ₀      =    initial quantity of the substance

t    =  time elapsed

$\rm t_{1/2}$    =    half life of the substance

The data given in the question is N ₀ = 800 moles , N(t)= 100 , t= 24 hours

$\rm t_{1/2} =\; ?$

Substituting values in the equation

$\rm 100 = \; 800 \;(\dfrac{1}{2} )^{\frac{24}{t_{1/2} } }$

$\rm \dfrac{100}{800} = \;(\dfrac{1}{2} )^{\frac{24}{t_{1/2} } }\\\\\rm \dfrac{1}{8} = \;(\dfrac{1}{2} )^{\frac{24}{t_{1/2} } }\\\\\rm (\dfrac{1}{2})^{3} = \;(\dfrac{1}{2} )^{\frac{24}{t_{1/2} } }\\\\\rm 3=\dfrac{24}{t_{1/2} }\\\\t_{1/2}= \dfrac{24}{3}\\\\t_{1/2} = 8 hours$

Therefore half life of the substance is 8 hours , Option D is the correct answer.

To know more about Half Life

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