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Problem 55 Hard Difficulty

Strontium-90 in Milk In the years immediately following the explosion at the Chernobyl nuclear power plant, the concentration of $^{90} \mathrm{Sr}$ in cow's milk in southern Europe was slightly elevated. Some samples contained as much as 1.25 Bq/L of $^{90}$ Sr radioactivity. The half-life of strontium- 90 is 28.8 years.
a. Write a balanced nuclear equation describing the decay of $^{90} \mathrm{Sr}$
b. How many atoms of $^{90} \mathrm{Sr}$ are in a 200 -mL glass of milk with $1.25 \mathrm{Bq} / \mathrm{L}$ of $^{90}$ Sr radioactivity?
c. Why would strontium- 90 be more concentrated in milk than other foods, such as grains, fruits, or vegetables?

Answer

a. ${ }_{38}^{90} \mathrm{Sr} \rightarrow{ }_{-1}{ }^{0} \beta+{ }_{39}^{90} \mathrm{Y}$
b. $3.28 \times 10^{890} \mathrm{Sr}$
c. calcium.

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Video Transcript

Let's try to do some calculations to identify the radiation exposure off strontium 90 so soon after the turn of your nuclear power plant explosion, the concentration off strongly of 90 in cow's milk from slightly increased in southern Europe. And then some sambas of milk condemned early video activity levels as high as bond flying to five. The girl leader off milk. And, uh, they're looking at the isotope strontium 90 and has 1/2 life equal to 28.8 years. So let's keep this information in mind to do some calculations about this, um, incident so that start with figuring out the balance nuclear equation. But the DK off strong damn mind so strongly in line D oh, you can tell from its really high mass number. Combat to its atomic number is new. Ground bridge being neutron midget will undergo be dedicated to farm you jam 90 The atomic number 39. So this is the balanced nuclear reaction. But decay off strong cam 90. Now it's time to calculate from the number off John D. M. 90 a terms in 200 milliliters off milk. So we were told that the, uh, radio activity is 1.25 becquerel per liter in this somber, if that is the case. But is the radio activity off 200 milliliters off milk? So the daughter read, Your activity is equal to run by. Do for big arose for a leader large applied by the quantity off milk. This days it's 200 milliliters are 2000.2 leaders. So you have you get wind tool five Baker. Okay, answer. You know this we can use the relationship between the half life and the the carrion constant to calculate decorated constant. So we can finally guy to let the number off strontium 90 others in the south. So the harsh life DeHoff is equal to find 69 30 over the decay rate constant. So the decay rate constant is going to be equal to the the constant 0.693 divided by that Haftar. Right? But we have to substitute the half life here in seconds. Units. So we have to first gun road brandy aid for in eight years. Two seconds. To do this, we have to multiply this by 3 65 days. But you, 24 hours Gardez, 60 minutes. Uh, and 60 seconds per minute. Once we do this simplification, we get the half life we can stop to do did here. So the hard drive is equal door nine. The kind 08 turning stone into the barber age sick. It's so once we simplify this, we can calculate the decayed constant and that it's going to be equal. Toe seven point 63 Time standard The negative 10 per second. So the sister decorated constant for this, um, strontium 90 bisexual. So let's move on to the next debt. Well, we used the relationship between the radioactivity game, which can be given in becquerel units, the decayed constant key, the number we just calculated, and the number who strongly imagines in this case. So we know the radio activity, even or the kids, and we can calculate in based on that so and has to be equal to the radio activity divided by the decree. It constant. So the radioactivity to be calculated is trying to five bicker uh, the care units classical so one becquerel is equal to bond decay. Brassica. So this is a little, um they kept per second is equal to becquerel units and we have to divide this by the degenerated constant that be calculated, which is someone find 63 times 10 to the negative 10 plastic. I mean, this surgeon last that he have three burned to aid turns into the farmer eight, Strontium 90 from Adams. Okay, the final question asks us by strontium 90 is more concentrated in milk than any other foot are such as grains, fruits, our Reggie difference. So, Mick, as you are probably have heard, is ah source afford that is rich in Cassie, right? So strong. Tm 90 actually strong Damn atoms are very similar to calcium atoms. They are on the same column in the periodic table, right? So they fall into the same group. And so they are very similar to each other. For that Jesus on the calcium in the milk can get you placed. Die stern. Damn Zain. So the other sources the question men sent mentions like grain, fruits and vegetables are not rich in calcium, but milk is so because this is the case. Strontium 90 can replace calcium. And that is right. Uh, milk has a high concentration off strontium 90. Unlike doctor oh, food sources

University of South Carolina - Columbia
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