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(a) Given that the decay constant for Radium is $-0.000428 /$ year, what will be left of a 10 gram sample of Radium after 200 years? (b) What is the half life of Radium? (c) What does this suggest to you about the safety of the dumping of Radium in our environment?

(a) 9.17961 grams(b) 1620 years

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 7

Applications of Exponential and Logarithmic Functions

Missouri State University

Idaho State University

Lectures

02:14

Radium decays by about $35…

01:46

(a) The half-life of radiu…

01:18

Radium Decay The amount of…

04:23

The half-life of radium is…

04:15

Half-Life The half-life of…

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The half-life of radium-22…

07:36

01:30

The amount of radium 226 r…

01:44

working with the uh substance radium, we are given its decay constant of negative 0.4 to eight. And we want to find how much of this will be left in 200 years. We started with a 10 g sample and what is its half life. So, I think it's easier here to actually start with part B calculating its half life. So, we have that the formula is for a half life is Ellen two divided by K. Which is its decay constant. So we have 0.0004-8, which gives us a half life for radium of 1,619 years and a half years. All right. So now finding the amount of this 10 g sample left in 200 years is pretty straightforward with that half life. We're gonna need to find this N piece right here. So, it's this number of half lives. So, let's go ahead and do this up here. So, and will be equal to we have these 200 years that have surpassed divided by its half life which is 1000 619 and a half years that we just found. Which gives us that over these 200 years, 0.12345/2 lives have passed. So only just more than 1/10 of a half life has gone by. Let's go ahead and use this first formula here. So this ending amount, that's what we're trying to find. I'm just going to refer to that as a Which is equal to our starting amount which is this 10g, Dividing that by two to the number of half lives. Which we just found to be 0.12345/2 lives. Let's go ahead and then just plug that into our calculators. And we see that the amount that will be left with this 10 g sample in 200 years is 9.179 g. And then part C. Is just asking us, what does this tell us if anything about the environmental safety, about dumping radium into the environment? Well, considering that the half life is 1600 years and that over 200 years, there's still nine g of this 10 g sample left, It sounds like it's really not good for the environment. So this environmental safety, I'm just going to say that it would be very bad for the environment, considering that it has a half life, as long as it doesn't, it would take that long for it to actually decay.

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