The half-life of 131 I is 8.04 days. (a) Convert the half-life to seconds. s (b)

Question

The half-life of 131I is 8.04 days. (a) Convert the half-life to seconds.
s

(b) Calculate the decay constant for this isotope.
s-1

(c) Convert 0.46 µCi to the SI unitthe becquerel.
Bq

(d) Find the number of 131I nuclei necessaryto produce a sample with an activity of 0.46 µCi.
131I nuclei

(e) Suppose the activity of a certain 131I sample is6.90 mCi at a given time. Find the numberof half-lives the sample goes through in 40.2 d and the activity atthe end of that period.
half-lives
mCi (a) Convert the half-life to seconds.
s

(b) Calculate the decay constant for this isotope.
s-1

(c) Convert 0.46 µCi to the SI unitthe becquerel.
Bq

(d) Find the number of 131I nuclei necessaryto produce a sample with an activity of 0.46 µCi.
131I nuclei

(e) Suppose the activity of a certain 131I sample is6.90 mCi at a given time. Find the numberof half-lives the sample goes through in 40.2 d and the activity atthe end of that period.
half-lives
mCi

Explanation / Answer

The half-life of 131I is t = 8.04 days.                                    = 8.04 * 24 * 60 * 60                                    = 694656 seconds                                    = 8.04 * 24 * 60 * 60                                    = 694656 seconds Decay constant, = 0.693 / t                            = 0.693 / 694656                            = 9.976 * 10 -7 sec -1 Convert 0.46 µCi to the SI unitthe becquerel = 0.46 * 10 ^ -6 Ci                                                                     = 0.46 * 10 ^ -6 * 37 * 10 ^ 9 Bq                                                                     = 17.02 * 10 ^ 3 Bq (d). Activity A = N So, No.of 131I nuclei necessary to produce a sample with anactivity of 0.46 µCi is N = A/                                                                                                                                  = 0.46 Ci /9.976* 10^ -7                                                i.e. N = 0.46 * 10 ^ -6 * 37 * 10 ^ 9 / ( 9.976 * 10 ^-7 )                                                          = 1.70609 * 10 ^ 10 Convert 0.46 µCi to the SI unitthe becquerel = 0.46 * 10 ^ -6 Ci                                                                     = 0.46 * 10 ^ -6 * 37 * 10 ^ 9 Bq                                                                     = 17.02 * 10 ^ 3 Bq (d). Activity A = N So, No.of 131I nuclei necessary to produce a sample with anactivity of 0.46 µCi is N = A/                                                                                                                                  = 0.46 Ci /9.976* 10^ -7                                                i.e. N = 0.46 * 10 ^ -6 * 37 * 10 ^ 9 / ( 9.976 * 10 ^-7 )                                                          = 1.70609 * 10 ^ 10

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