Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 12
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A Sample Contains a Mixture of 108ag and 110ag Isotopes Each Having an Activity of 8.0 × 108 Disintegration per Second. 110ag is Known to Have Larger Half-life than 108ag. - Physics

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Question

A sample contains a mixture of 108Ag and 110Ag isotopes each having an activity of 8.0 × 108 disintegration per second. 110Ag is known to have larger half-life than 108Ag. The activity A is measured as a function of time and the following data are obtained.
 

Time (s)

 
Activity (A)
(108 disinte-
grations s−1)
Time (s)

 
Activity (A
108 disinte-grations s−1)
20
40
60
80
100
11.799
9.1680
7.4492
6.2684
5.4115
200
300
400
500
 
3.0828
1.8899
1.1671
0.7212
 


(a) Plot ln (A/A0) versus time. (b) See that for large values of time, the plot is nearly linear. Deduce the half-life of 110Ag from this portion of the plot. (c) Use the half-life of 110Ag to calculate the activity corresponding to 108Ag in the first 50 s. (d) Plot In (A/A0) versus time for 108Ag for the first 50 s. (e) Find the half-life of 108Ag.

Solution

(a) Activity, A0 = 8 × 108 dis/sec

(i) `"In" (A_1/A_0) = "In" (11.794/8) = 0.389`

(ii) `"In" (A_2/A_0) = "In" (9.1680/8) = 0.12362`

(iii) `"In" (A_3/A_0) = "In" (7.4492/8) = -0.072`

(iv) `"In" (A_4/A_0) = "In" (6.2684/6) = -0.244`

(v) `"In" (A_5/A) = "In" (5.4115/8) = -0.391`

(vi) `"In" (A_6/A_0) = "In" (3.0828/8) = -0.954`

(vii) `"In" (A_7/A_0) = "In" (91.8899/8) = -1.443`

(viii) `"In" (1.1671/8) = "In" (90.7212/8) = -1.93`

(ix) `"In" (0.7212/8) = "In" (90.7212/8) = -2.406`

The required graph is given below.

(b) Half-life of 110Ag = 24.4 s
(c) Half-life of 110Ag,  `T_"1/2"`= 24.4 s

Decay constant, `lambda = 0.693/T_"1/2"`

⇒ `lambda = 0.63/24.4 = 0.0284`

`therefore t = 50 sec`

Activity , `"A" = "A"_0e^(-lambdat)`

= `8 xx 10^8 xx e^(-0.0284 xx 50)`

= `1.93 xx 10^8`

(d)

(e) The half-life period of `""^108"Ag"` that you can easily watch in your graph is 144 s .

  Is there an error in this question or solution?

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Solution A Sample Contains a Mixture of 108ag and 110ag Isotopes Each Having an Activity of 8.0 × 108 Disintegration per Second. 110ag is Known to Have Larger Half-life than 108ag. Concept: Radioactivity - Introduction of Radioactivity.
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