Answer:
Incomplete questions
This is the complete question
The half-life of a radioactive isotope is the time it takes for a quantity for the isotope to be reduced to half its initial mass. Starting with 150 grams of a radioactive isotope, how much will be left after 6 half-lives
Explanation:
Let analyse the question generally first,
The the mass of the radioactive element be M.
We want to know it mass after n half life
Then,
After first half life, it mass is
M1=M×½
After second half life, it mass is
M2= M×(½)²
After third half life, it mass is
M3= M×(½)³
But now we can see a pattern developing, because for each new half-life we are dividing the quantity by 2 to a power that increases as the number of half-lives.
Then we can take the original quantity and quickly compute for
nth half-lives:
So after nth half life will be
Mn= M × (½)ⁿ
Generally,
Now, let apply it to our questions
Give that the mass of the radioactive isotope is 150grams
It mass after 6th half life
Then, n=6
So applying the formula
Mn= M × (½)ⁿ
M6= 150 ×(½)^6
M6= 150×1/64
M6=2.34grams
The mass of the radioactive isotope after 6th half life is 2.34grams
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= speed of sound in the rod =
= times interval between the hearing the sound twice = 0.12 s
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= time taken by the sound to travel through the rod
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