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Problem 26 Easy Difficulty

On March 11, 2011, a magnitude 9.0 earthquake struck northwest Japan. The tsunami that followed left thousands of people dead and triggered a meltdown at the Fukushima Daiichi Nuclear Power Plant, releasing radioactive isotopes $^{137} \mathrm{Cs}$ and $^{134} \mathrm{Cs}$ among others, into the atmosphere and into the Pacific Ocean. By December 2015 (about 1 730 days after the meltdown), contaminated seawater reached the U.S. west coast with maximum Cs activities (including both isotopes) per cubic meter of seawater reaching 11.0 Bq/ m3 , more than 500 times below the U.S. government safety limits for drinking water. The half - lives of $^{137} \mathrm{Cs}$ and $^{134} \mathrm{Cs}$ are $1.10 \times 10^{4}$ days and 734 days, respectively. Calculate the number of (a) $^{137} \mathrm{Cs}$ and (b) $^{134} \mathrm{Cs}$ nuclei in the 1.00 $\mathrm{m}^{3}$ seawater sample, assuming $^{137} \mathrm{Cs}$ and $^{134} \mathrm{Cs}$ were originally released in equal amounts.

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Top Physics 103 Educators
LB
Liev B.

Numerade Educator

Marshall S.

University of Washington

Aspen F.

University of Sheffield

Meghan M.

McMaster University

Video Transcript

{'transcript': "Okay, so in this question, they tell us the half of season 1 37 is 30.2 years. So T half life is equal to 30.2 years. Now. They tell us that they want us to calculate how long it will take for the radio activity of this radio nuclear to decay to 5% off the level released in 2011. Right. So the question that we need is path to the end is equal to the amount left and the amount left has to be in decimal form. So we have the community percent into decimals and n is the number of half life that has passed. So let's start. So we have half and it's equal to what is the amount left? Well, they want us to calculate how long it would take for indicated 5% of the initial level. So that means that the amounts left is 5% which is 50.5 right? We gotta converted to festivals and 5% divided by 100 which is the conversion of percent of decimals is 1000.5 now, in order to Eisley end as essence and is a exponents we can take the lager both sides by one of the properties. A lot as I retake the log of something than the exponents is brought to the front. So pretty much we just multiply into now. All right, so if we walk one side, we're gonna log both sides. So let's divide both sides by allows a one half now across out log. And now we have em. It is equal to 4.32 So this is the number of half life that has passed, right? And they tell us the half life is 30.2 years. So all we gotta do is take 4.32 and multiply it by 30.2 and we get 100 dirty 0.52 years."}

SUNY University at Buffalo
Top Physics 103 Educators
LB
Liev B.

Numerade Educator

Marshall S.

University of Washington

Aspen F.

University of Sheffield

Meghan M.

McMaster University