Question

TH 100 - D100 Use equation : acca un Page 4 of 5 4. Suppose we have Xo amount of a certain radioactive substance. It has been observed that this substance losses 5% of its mass every 10 years. @ How much of the initial mass Xo remains after 10 years? What about 20 years? (b) Use the answer to part (a) to write down an appropriate exponential model that describes the amount of the radioactive substance left after t years. 3] (c) Determine the half-life of this substance. Leave your answer in "calculator ready form.

h= half life

a0 = original amount

a(t) = amount present after t years

t = time

What information do you need?

Answer 1

@ der A - Product to No at t= 10 yrs 5% of Xo = 0.0520 Offer 10 yos Substance seniain = 20-0.05%. = 0'95 Ko Ang Also enery 10 yas substance decay Sr. of its masses left. then aftest 20 yos, mass left will be=0.95%, -5% of 0.95% = 0.95X0 – 0.0475X. (After 20 yos = 0.9025%) and ☺ According to Radiancine decay cow, UN N = (N= No ent] -0 No where; N = number of radioactive nuclie remaning at any timet No: radioactie. nullie at time tso d = decay constant As, substance losses 5% of its mass eury loyos then from egn ☺ In 0195ko = -0.10 do a= - 1n 0.95 To

of the radiactive substance left after tyos, Now, amount is given by ? No=a.ordt 2 where Id=-1no.gg = 5x103 10 © Half life, (h) = 1n2 = 102 58103 . Peste 2 5x10-3 = 0.693 3 20 220693 = 0·1386x103 h = 138.6 yo
In part (a) answer of 20 years can also be solved by radioactive law equation that is in part (b).

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