A radioactive sample contains 2.50µg of pure 11 C, which has a half-life of 20.4

Question

A radioactive sample contains 2.50µg of pure 11C, which has a half-life of 20.4 min. (a) How many moles of 11C arepresent initially?
mol

(b) Determine the number of nuclei present initially.
nuclei

(c) What is the activity of the sample initially?
Bq

(d) What is the activity of the sample after 6.00 h?
Bq (a) How many moles of 11C arepresent initially?
mol

(b) Determine the number of nuclei present initially.
nuclei

(c) What is the activity of the sample initially?
Bq

(d) What is the activity of the sample after 6.00 h?
Bq

Explanation / Answer

For (a) n = m/M = (2.50*10-6)/11 = 2.27*10-7 mol For (b) N0 = nNA       =(2.27*10-7)(6.02*1023) =1.368*1017 nuclei For (c) R0 = N0 =(N0ln2)/T1/2 = [(1.368*1017)ln2]/[(20.4)(60)] = 7.747*1013 For (d) R = R0e-(tln2/T1/2) =(7.747*1013)e^[-{[(6ln2)]/[(20.4)*(1/60)]}] = _____Bq

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