Generate solvely question under radioactivity and provide their answer
Physics
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6 stepsQuestion:
A sample of a radioactive isotope has an initial mass of 200 g. After 10 days, 50 g of the isotope remains. What is the half-life of the isotope?
Answer:
The formula relating the remaining mass of a radioactive isotope to its half-life is:
N(t) = N₀ * (1/2)^(t / T)
where:
N(t) is the mass remaining after time t
N₀ is the initial mass
t is the time elapsed
T is the half-life
Identify the given values.
N₀ = 200 g
N(t) = 50 g
t = 10 daysSubstitute the values into the formula.
50 g = 200 g * (1/2)^(10 days / T)
Isolate the term with the half-life.
(50 g) / (200 g) = (1/2)^(10 days / T)
(1/4) = (1/2)^(10 days / T)Express both sides with the same base.
(1/2)² = (1/2)^(10 days / T)
Equate the exponents.
2 = (10 days) / T
Solve for T.
T = (10 days) / 2
T = 5 daysThe half-life of the isotope is 5 days.
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