how long would it take for 2.8 micrograms of a 10.4 micrograms sample of Pa to d
ID: 1066445 • Letter: H
Question
how long would it take for 2.8 micrograms of a 10.4 micrograms sample of Pa to decay? the half-life of Pa is 3.25x10 ID: A Class a Date ID: A Name C 12. How long would it take micrograms of a 10.4 microgram sample of Pa to decay? The half life for 2.8 231 Pa is 3.25 x 104 y a. 1.2 x 105 y years b. 6.2 x 104 y No. 10 M c. 1.5 x 104 y d. 8.1 x 106 y e. 4.0 x 105 y reactions represents fission? 13. Which one of the following 246 238 98 a. 92 C B He 233 Pa -1e 233 Ba 3 on 90 146 La 35 on 235 57 92 He AnExplanation / Answer
Ans. Ans. Using the formula: ln (At / Ao) = - kt - equation 1
ln (A0 / At) = kt - equation 2 (equation 1 rearranged)
Where,
Ao = Initial amount
At = Amount remaining at time t
k = rate of disintegration (radioactivity)
t = time duration of radioactivity
Given,
Initial amount (Ao) = 10.4 ug
Amount decayed = 2.8 ug
Amount remaining (At) = Initial amount – amount decayed = 10.4 ug – 2.8 ug = 7.6 ug
Half-life = 0.693 / k
Or, k = 0.693 / half-life = 0.693 / (3.25 x 104 y) = 2.1323 x 10-5 y-1
Putting the values in equation 2
ln (10.4 ug/ 7.6 ug) = (2.1323 x 10-5 y-1) x t
or, ln (1.368) = (2.1323 x 10-5 y-1) x t
or, 0.31365755886 = (2.1323 x 10-5 y-1) x t
or, t = 0.31365755886 / (2.1323 x 10-5 y-1) = 0.147 x 105 y
hence, t = 1.47 x 104 y = 1.5 x 104 y (approx.)
Correct option. c. 1.5 x 104 y
Ans. A fission reaction involves splitting of a nucleus into two or more lighter nuclei.
U235 (superscript indicates mass) splits into two lighter nuclei – La146 and Ba87
Hence, Correct option. d.
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