81Rb decays to the metastable state of 81Kr as shown. The half life of 81Rb is 4

Question

81Rb decays to the metastable state of 81Kr as shown.
The half life of 81Rb is 4.58 hours. The half life of the
metastable state of 81Kr is 13 seconds. Krypton is an
inert gas. 81mKr is used to assess the lung function,
measuring the number of emitted gamma rays on a
breath by breath basis. A breath clears the amount of
81mKr.
ONLY NEED PART II. (ANSWER FOR PART ONE IS 1.103 * 10^3 Bq)
(i) Assuming that an 81mKr activity of 1.4 MBq is required to be available 30 seconds later, before next breath; what activity of 81Rb must be present at the start of the 30 second period?

(ii) What activity of 81Rb must there have been 18 hours earlier, when 81R was first produced?

Explanation / Answer

Half life of 81 Rb is   T 1/2   = 4.58 hours Decay constant of 81Rb                                     =   ( 0.693 ) / T 1/2                                      = ( 0.693 ) / ( 4.58 hours )                                   = 0.151 hour -1   Activity of the sample after time t is                  A   = A o e - t    Here A o is the initial activity of the sample .        A is final activity of the sample ( Activity of the sample after time t )         t is time of decay. Here you asked initial activity of the sample of 81 Rb( when it was first produced ) . But you didn't given the activity of the sample after 18 hours.   _________________________________________________________________________________________________________________ Another case: If you want the initial activity of the sample. If m is the initial mass of 81 Rb Number atoms present in 81 Rb is                  N = ( m in grams / 81 ) (6.023*1023 atoms / mol) Then Initial activity of the sampleis                  A o = N   in Bq Here A o is the initial activity of the sample .        A is final activity of the sample ( Activity of the sample after time t )         t is time of decay. Here you asked initial activity of the sample of 81 Rb( when it was first produced ) . But you didn't given the activity of the sample after 18 hours.   _________________________________________________________________________________________________________________ Another case: If you want the initial activity of the sample. If m is the initial mass of 81 Rb Number atoms present in 81 Rb is                  N = ( m in grams / 81 ) (6.023*1023 atoms / mol) Then Initial activity of the sampleis                  A o = N   in Bq

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