9.) The isotope chromium-51 has a half-life of 28 days. If the original sample had a 51Cr mass of 32.0 grams, what mass of 51Cr would remain after 84 days
2 answers:
Answer:
Explanation:
The half-life of chromium-51 (28 da) is the time it takes for half of it to decay.
After one half-life, half of the original amount will remain.
After a second half-life, half of that amount will remain, and so on.
We can construct a table as follows:
We see that, after 84 da (three half-lives), ⅛ of the original mass remains.
Answer: The mass of Cr-51 present at 84days = 4.00g
Explanation: Using the relation
Nt/No = e -( kt)
Where
Nt = mass remain at time t(days)=?
No= initial amount at time zero= 32.0g
K= decay constant
t = 84 days
T1/2 = Half life= 28days
k= In 2/ (T1/2)
In 2 =0.693
Which implies
k = 0.693/28
k= 0.02475 per day
Nt = No e-(Kt)
Nt = 32 e- ( 0.02475 × 84)
Nt = 32 e-(2.079)
Nt = 32 × 0.125
Nt=4.00g
Therefore the mass of Cr-51 remaining after 84days is 4.00g
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