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
[tex]\rm N(t) = \; N_{0} \;(\dfrac{1}{2} )^{\frac{t}{t_{1/2} } }[/tex]
N(t) = quantity of the substance remaining
N ₀ = initial quantity of the substance
t = time elapsed
[tex]\rm t_{1/2}[/tex] = half life of the substance
The data given in the question is N ₀ = 800 moles , N(t)= 100 , t= 24 hours
[tex]\rm t_{1/2} =\; ?[/tex]
Substituting values in the equation
[tex]\rm 100 = \; 800 \;(\dfrac{1}{2} )^{\frac{24}{t_{1/2} } }[/tex]
[tex]\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[/tex]
Therefore half life of the substance is 8 hours , Option D is the correct answer.
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