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For the radioactive isotope 131I, the time required for 50% disintegration is 8 days. The time required for the 99.9% disintegration of 5.5g of 131I is __________ days, (up to one decimal place):
Correct answer is between '79,81'. Can you explain this answer?
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Explanation:
Half-life of 131I:
The time required for 50% disintegration of a radioactive isotope is known as its half-life. The half-life of 131I is given as 8 days.
Calculating the decay constant:
The decay constant is denoted by the symbol λ and is used to determine the rate of decay of a radioactive isotope. It is calculated using the formula:
λ = 0.693/t1/2
where t1/2 is the half-life of the isotope.
Substituting the values of t1/2 and solving, we get:
λ = 0.693/8 = 0.086625
Calculating the time required for 99.9% disintegration:
The time required for 99.9% disintegration of an isotope can be calculated using the following formula:
N/N0 = e^(-λt)
where N is the final amount of the isotope, N0 is the initial amount of the isotope, e is the base of natural logarithms, λ is the decay constant, and t is the time.
Substituting the given values, we get:
N/N0 = 0.001
λ = 0.086625
N0 = 5.5g
0.001 = e^(-0.086625t)
Taking natural logarithm on both sides, we get:
ln(0.001) = -0.086625t
Solving for t, we get:
t = 80.2 days
Therefore, the time required for the 99.9% disintegration of 5.5g of 131I is 80.2 days (up to one decimal place).
Final Answer:
The time required for the 99.9% disintegration of 5.5g of 131I is 80.2 days (up to one decimal place).
Half-life of 131I:
The time required for 50% disintegration of a radioactive isotope is known as its half-life. The half-life of 131I is given as 8 days.
Calculating the decay constant:
The decay constant is denoted by the symbol λ and is used to determine the rate of decay of a radioactive isotope. It is calculated using the formula:
λ = 0.693/t1/2
where t1/2 is the half-life of the isotope.
Substituting the values of t1/2 and solving, we get:
λ = 0.693/8 = 0.086625
Calculating the time required for 99.9% disintegration:
The time required for 99.9% disintegration of an isotope can be calculated using the following formula:
N/N0 = e^(-λt)
where N is the final amount of the isotope, N0 is the initial amount of the isotope, e is the base of natural logarithms, λ is the decay constant, and t is the time.
Substituting the given values, we get:
N/N0 = 0.001
λ = 0.086625
N0 = 5.5g
0.001 = e^(-0.086625t)
Taking natural logarithm on both sides, we get:
ln(0.001) = -0.086625t
Solving for t, we get:
t = 80.2 days
Therefore, the time required for the 99.9% disintegration of 5.5g of 131I is 80.2 days (up to one decimal place).
Final Answer:
The time required for the 99.9% disintegration of 5.5g of 131I is 80.2 days (up to one decimal place).
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For the radioactive isotope 131I, the time required for 50% disintegration is 8 days. The time required for the 99.9% disintegration of 5.5g of 131I is __________ days, (up to one decimal place):Correct answer is between '79,81'. Can you explain this answer?
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