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After two hours, 1/16 of the initial amount of a certain radioactive isotope remains undecayed. The half life of the isotope is
- a)15 minutes
- b)30 minutes
- c)45 minutes
- d)60 minutes
Correct answer is option 'B'. Can you explain this answer?
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After two hours, 1/16 of the initial amount of a certain radioactive i...
Explanation:
Let's assume that the initial amount of radioactive isotope is 'x'.
After 2 hours, 1/16 of the initial amount remains undecayed.
Therefore, the amount of decayed isotope = x - 1/16x = 15/16x
Let's find the time required for half of the isotope to decay.
Half of the initial amount = 1/2x
Let the time required for half of the isotope to decay = t
According to the formula for radioactive decay, the amount of isotope remaining after time 't' can be given as:
Amount of isotope remaining = initial amount x (1/2)^(t/half-life)
Substituting the values, we get:
1/2x = x x (1/2)^(t/half-life)
1/2 = (1/2)^(t/half-life)
1 = 2^(t/half-life)
t/half-life = 0
Therefore, the half-life of the isotope is 30 minutes (option B).
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After two hours, 1/16 of the initial amount of a certain radioactive isotope remains undecayed. The half life of the isotope isa)15 minutesb)30 minutesc)45 minutesd)60 minutesCorrect answer is option 'B'. Can you explain this answer?
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