a) $$m(t)=100 imes(2)^-fract30$$b) $$9.92 mathrmmg$$c) $$199.3$$d) about after $<199.3>$ years, the sample will certainly remain just 1 $mathrmmg$




You are watching: The half life of cesium 137 is 30 years suppose we have a 100 mg sample

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Video Transcript

now for trouble on Percival. It's they ns m f t If the chaos off season in Medic Rams continuing to be after time t in years, for this reason am v T is same to a many zero. The phone article season at years here, multiply by exponential Okay, key. So Mosul is providing to it is in 100 milligrams exponential k g. Currently you require to acquire the worth of K for this reason it's the kink it the article season at any year t therefore first, to acquire the value off K, us have an additional giving the the half life of caesium is 30 years. For this reason a month 30 is actually equal toe have off the of deal. So ns am a 30 is same to 100 exponential Okay, marked by by search shedding this 2 room and also the half life cesium is have actually multiplied through 100. Oh, we have the right to terminate this with 100 through this 100. Therefore we have hey 13 d same toe 1/2 and we can't take then both sides. So right here we will have 30 k amounts to to lend Hey and let fifty percent is additionally equal toe an unfavorable Len device for simplicity. Therefore the K worth would be negative men to end 30. And also now we have the right to say that ns am through T is the mess it in right here is equal to 100 exponential. Negative. Then toe end 30 gay T shirt over certainty. Okay. And also this deserve to be simplified that a mufti is equal toe 2200. Sorry, 200 v the strength off an adverse t over 3rd cause exponential lento is equal to come So right here we have 200. So currently we have gained that The main function so was part B. We desire I don't understand after 20 is same to 100 exactly how much mace stays So we basically saying am off 100 tired Substitution is same toe 200 v the dollar off an unfavorable 100 over search which is same pool around 9.92 countless grapes currently was component See friend will try to acquire the rate of degeneration So us will start by utilizing the because that the attributes that we have gained Wife he's equal. Perform we will have actually 20 200 Sorry. 5 t equals 200 through the park. An unfavorable t over 30. Therefore why dish 50 which is a decay over time. At any year, T is same to 200 through the power of negative T over 30 multiply by an unfavorable one over 13 allow me to. And also now at year 100 Why dash 100? The price of decay exactly as a year. 100 is equal toe 100 Oh, I'm sorry. Is same to 200 through the power of an unfavorable 100 over 30 multiplied by negative one over 30 point to i beg your pardon is same to an adverse Whole point to to nine milligram to be you the is only logical is the negative value your prisons the it is a decayed that is a shedding mess and also this worth is just how much mess will be lost at year 100. So this is great. How much milligrams once the cesium lose at year Betty and also this and also this street is at her 100 currently for part d you desire to gain when v why 50? as soon as will it it is in equal? just one milligram. So us will relocate like backward. Obtain the value or five t the is same toe one milligram. Therefore we will certainly say the 100 however we will take one step ago will be much easier. 100 e through the power of an adverse lento over 30 g. So instead of utilizing the value of 100 us took a step ago using this exponential off negative then and also that is equal No. One. It's divide both political parties by 100 giving us e to the harbor of an adverse lento end 30 de same cool, one end 100 and we will certainly take victory for both sides. So here we have an unfavorable Lynn over 30 de equal device Lynn one end 100. And also now us can acquire value can get the value of T the year at which decision will be one milligram and that is equal to year 100 99 go three. For this reason it will certainly take decision around two centuries to degeneration from 100 milligram toe, just one milligram. Say thanks to you