5

Thc gencnl equation that models radioactive decay of = substance is A() = I00 1The equation6290 A(t) = I0 2 VAS used recently t0 find the present-day radioactivity...

Question

Thc gencnl equation that models radioactive decay of = substance is A() = I00 1The equation6290 A(t) = I0 2 VAS used recently t0 find the present-day radioactivity of some wooden tools at anarchaeological dig: What does the number 6290 represent?lab has 450 grams of an unknown radioactive substance. The curve below shows the mass of the substance recorded each minute. Approximately how many grams of the substance remain after minutes?IuWhat is the decay rate of the substance whose decay modelle

Thc gencnl equation that models radioactive decay of = substance is A() = I00 1 The equation 6290 A(t) = I0 2 VAS used recently t0 find the present-day radioactivity of some wooden tools at an archaeological dig: What does the number 6290 represent? lab has 450 grams of an unknown radioactive substance. The curve below shows the mass of the substance recorded each minute. Approximately how many grams of the substance remain after minutes? Iu What is the decay rate of the substance whose decay modelled by the following equation? S() 820(0.531 A red shirt loses 7% of its colour every time is washed. Create model of exponential decay for C(w), the percent of colour remaining alier washings:



Answers

Radioactive Decay The amount of a radioactive substance decreases exponentially, with a decay constant of 3$\%$ per month.
(a) Write a differential equation to express the rate of change.
(b) Find a general solution to the differential equation from part (a).
(c) If there are 75 $\mathrm{g}$ at the start of the decay process, find a particular solution for the differential equation from part (a).
(d) Find the amount left after 10 months.


Newton's Law of Cooling Newton's law of cooling states that the rate of change of temperature of an object is proportional to the difference in temperature between the object and the surrounding medium. Thus, if $T$ is the temperature of the object after $t$ hours and $T_{M}$ is the (constant) temperature of the surrounding medium, then
$$\frac{d T}{d t}=-k\left(T-T_{M}\right) $$
where $k$ is a constant. Use this equation in Exercises $61-64$

This problem, we're going to be dealing with exponential decay. Um And we know that this is gonna be a. F. T. Is equal to a not E. To the Katie. We're now R. K. Is going to be a negative constant. We see after six hours the mass had decreased by three and we have an initial mass of 200. If it decreased by 3% we now have 3%. We now have 97 Of 200, which is going to be 194. So then we're gonna divide by 200. And then we see that the time it took for this to occur with six hours at the natural log on both sides. And that gives us this, then you divide by six mm. And we end up getting that R. K. Value is going to be this small negative number. But this helps because now when it comes to this we have 200 here and now we have our model for the exponential decay.

This question is giving us a mathematical model which is representing the decay of radioactive substances. You can see that written here where Q. Is equal to Q. Note times E. To the power of our times T. Were also given the rate of decay as negative 0.0004332. This for purposes of our formula is equal to this is our our variable. What were asked is how long will it take to decay to half of the original amount? And it sounds a little difficult considering all we've been given is the rate. But really we can just plug in any values for Q. And Q. Notes. So long as it's following this half life ideal. Right? Because we're decaying to half of the original amount. So let's assume that we started with say two to whatever it is. Okay. Which means by the time we have decayed to half Q. Will have to be one because it's half of our original. Let's start to plug the, since we have one will be equal to two times E. We have our rate which was given to us to be negative 0.0 433, 2 times T. And T. Is what we're looking for right? We want to know how long it's going to take. So let's start to simplify this, we can get down to T. So starting by dividing both sides by two, we'll get 0.5 on the left hand side is equal to E. To negative 0.4332 times teeth. But now we somehow need to get T out of that exponents so that we can actually solve for it, meaning we need to take the natural log of both sides By doing that, we get Ln Times 0.5 on the left hand side. By taking the natural log of the right hand side. We get to get rid of E. And bring down our exponents here. And now it seems pretty clear how we can solve for T. We just need to divide both sides by our decay rate. All right. So if we go ahead and do that, plug this left hand side and your calculator, we'll see that tea or our time to decay to half of the original amount of whatever substance this is, is about looks like 1600 years.

Okay, So for party, they say that we have americium 2 41 undergoes beta millions. That goes out for the case. I'll foot the Caisse for two. Alfa was for two helium, right? So the first thing that we got to do is determined the atomic number of a M. And we see that it's 95. So now we gotta balance your Tommy number and the atomic mass on both sides. So we have 95 other left. We have two on the right. This means we need 93 more on the right. So in 93 we see the element number 23 is MP. I believe that's Neptune IAM. And in the weight is to 41. And we have four on the right, so we must add 237. All right, so to 37. And this is the answer to part a. If a part b, we have americium 2 41 undergoes a bunch of Alfa and a bunch baited the case. So I counted. So we have to 41 immersing him so I can't. We have eight out of the case and we have forbade at the case. So we know it now for the case for two Alfa. And we know that beta decay is zero negative. One paid up, right? So from this we know that an Alfa decay decreases. Do you wait by four? And it decreases your talent number by to write. Since we have eight of them, we should decrease the weight by 32. And we should decrease the atomic number by 16. Now we know a beta decay increases the atomic number by one. And since we have four of them, we should increase the atomic number by four. Right? I'm not gonna write it like that. So we should increase the entire number by four. But since he has a weight of zero, it doesn't do anything to the mass. Right. So we have 2 41 2 41 And I said that it decreases have mass by 32 for the A alphas, right? And then the beta has no effect. So minus zero. And this gives us 209 as you wait. Right? So we need this value and then let's look at the atomic number. So we have 95 we say the Alfa particle decreases to your timeline number by 16. So the eighth increases by 16 and beta increases it by one. But we have four of them, right? So increased by four. And now we get 83. Right, So we have to nine in 83. So when we look at a period table, we see that element Number 83 is B. I business. So this is our answer now for party. I think they want us to write all the intermediates. So let's start. So we have 2 41 I am, and we know that is atomic number 95. So an Alfred Decay is number one. All right, so if we subtract the atomic number by two, we get 93. Anybody subtracting atomic mass by four, we get to 37. Why we get MP for that element. And now it's another Alfa decay, right? So we subtract four from the top. So we get to 33 this affect you from the bottom and get 91 and that is P A. Now it's fate of the K, right? So for beta decay has no effect underweight, but it adds one to D atomic number and that is uranium. And then we have another outfit. Decay. Right. So minus four minus two. So minus four on top is true. True. Nine minus two on the bottom is 90. So we get during him now for the next perch, we have another outfit. Decay. Right. So minus four. On the top, we get to 25 minus two. On the bottom, we get 88 That is for a And the next one is a beta decay. So no effect on the top. It's close, one on the bottom and we get a C as our element. Now, the next one is a hotfoot to came. So we have plus minus four on the top. So we have 2 to 1 and minus two on the bottom. So we have 87 and that is element. That's our. Now we have another outflow. Takei. So minus 2 94 on the bottom, I just minus four on the top, minus two on the bottom. So you have to 17 and we have 85 85 element 80. And now we have another outfit decay, right. Another outfit. The KC minus four on the top. You get to 13 minus two. On the bottom, we get 83 Element 83 is business. And now we have a beta decay. All right, so we have a bit of the K. So beta decay has no effect on weight. So we have the exact same late. So we have to 13 but it increases the time number by one. So we have 84 and that is P O. And then we have another outfit decay. So decreases topped by four. So we have 209 decreases bottom by two. We have 82 that is PB. And lastly, we have a beta decay, right? So does not affect the top, but increases the bottom by one. So 83 we are back to business. So we have to 93 business. And when we go all the way appear, we see that we also got to a 93 business. So that is

So in this problem let's show the decay of this. Yeah, isotope of America Yeah. Through alpha particle production. So if we look at the periodic table, you can see that this Element had atomic number 95. It's going to They met one alpha particle. So the alpha particle as a four for the mass number and two for the atomic number. So these two numbers need to add together to get this number. These two numbers on the bottom need to have to give the number on the bottom on the left. So let's just figure out what this number would be based off that you can see. 2 37 plus four gave us 2 41. So This is correct. And then bottom will be 93 because 93 plus two is 95. So now we have the isotope. And if we look at the periodic table, atomic number 93 gives us Neptune to me, um to n. p. So this would be the ice talk that results. So now let's look at the so now we have some successive decays here. So first as an alpha decay. So then that would just be the first thing that we wrote in a and then it's going this resulting new Clyde is going to it meant another alpha particles. So we're just going to do the same thing. If we do the math, you will find this is the resulting new client, then we'll use this and we see the next emission is a beta particle. So the beta particle is an electron. So what happens is with the electron zero is the number of top and negative one is number on the bottom. So we're going to have to add 12 This number and then we get 92 so 92 miles one standing one and then the number of top stays the same. So then atomic number 92 will give us your radio. So this would be the product. So after that we're going to do another alpha decay. So we've done that once more we get through you. So then after that another outfit case we have to al decay product again it was radio. And then After that that's a bit of the case. We're going to again through the base of the case. So we get atomic number 89 and then we'll do three out for the case that we do an alpha decay here, do you another alpha decay then another alpha decay. So now we've done the three alpha decays and then there's another beta decay. So it will be one more than the atomic number of the grafton. And then we have another alpha decay. This last one should actually be a beta decay. So go ahead and just make this a beta decay. Yeah, So let's find the top number 83. It's a good month. So that would be the final product. So let's just double check and make sure all the decades are correct. So we have one alpha, second alpha. So we have a very Doyle. Then we have alpha alpha. Then we have to but we have three offers in succession, 123. And then we have a data. We have another alpha and last one beta. So that's our final father and the Sustainable Nucleus. And the three intermediate new clients are just going to be basically what we formed in these each of these intermediate steps.


Similar Solved Questions

5 answers
1 unskensWhhich Tha 22 curyo I # 1 Sudo Jonmnba (ollotano oinar (0) Support your answer by graphirg of the potynomtal oeorod and the 3 1 Jopons benavior onthn L aoing polnomliTunclon li rght because Ihc Ioading iw N tuncuol { L 1 corcantis 1 llo Bcau 90 1E
1 unskens Whhich Tha 22 curyo I # 1 Sudo Jonmnba (ollotano oinar (0) Support your answer by graphirg of the potynomtal oeorod and the 3 1 Jopons benavior onthn L aoing polnomliTunclon li rght because Ihc Ioading iw N tuncuol { L 1 corcantis 1 llo Bcau 90 1 E...
5 answers
Problem 17.33Part A From Khat holhi was the50kr bontng bal at 0 C is droppu-d inlo Wb containing Mutunu Ic and waler: A shont tima !er when newcoumonuim hnsbnn Aaanlaneo Ihor ar5 0 Feda droppea? Assumo Ihat Wlor 0 splashes Out aignificant figures and include the approprlalo units.Exptesg YouranawcrValueUnitsGubmtllVy Anbror ckuun
Problem 17.33 Part A From Khat holhi was the 50kr bontng bal at 0 C is droppu-d inlo Wb containing Mutunu Ic and waler: A shont tima !er when newcoumonuim hnsbnn Aaanlaneo Ihor ar5 0 Feda droppea? Assumo Ihat Wlor 0 splashes Out aignificant figures and include the approprlalo units. Exptesg Youran...
5 answers
[2Opts] Prove each of the following: (a) If alb and a/c; then af(b _ c) (6) a =b (mod m) ^ c= d (mod m) = a+c=b+d (mod m)
[2Opts] Prove each of the following: (a) If alb and a/c; then af(b _ c) (6) a =b (mod m) ^ c= d (mod m) = a+c=b+d (mod m)...
5 answers
Viii) Use the Fundamental Theorem of Calculus to find the derivative of h(r) = Ginrvi-7 dx; osxs}
Viii) Use the Fundamental Theorem of Calculus to find the derivative of h(r) = Ginrvi-7 dx; osxs}...
2 answers
ThwCnztGuerclo % 4DIAm 01337*0 k miten Caaan olc 40J T Muict Z10nCaletlPatuUng Guret Ccenen 0toMntTun OcudO077nJCerHecuat Aiaetshorde eandneiJod7
thwCnzt Guerclo % 4 DIAm 01337*0 k miten Caaan olc 40J T Muict Z10n Caletl Patu Ung Guret Ccenen 0to Mnt Tun OcudO 077nJ Cer Hecuat Aiaet shorde eandnei Jod7...
5 answers
Provide a name for the compound below:
Provide a name for the compound below:...
5 answers
QUESTion 30 Ktech olutn tolamm rorIbans Van o tu (Yoatud riot have coud pumn" Uatnd = cwcuatnr 4t ' CMen AlaaS50,Xn 0x0) 50 Nr Fofal 42 046w) Fo( ) OcCit) SOxq} CaSoyl) Nalnl 02 00 IOskol Oo Wz Nata} Oz1 NOxq}
QUESTion 30 Ktech olutn tolamm rorIbans Van o tu (Yoatud riot have coud pumn" Uatnd = cwcuatnr 4t ' CMen Alaa S50,Xn 0x0) 50 Nr Fofal 42 046w) Fo( ) OcCit) SOxq} CaSoyl) Nalnl 02 00 IOskol Oo Wz Nata} Oz1 NOxq}...
5 answers
Predict which member of each group is most soluble in water, and explain the reasons for your predictions.(a) 1 -butanol, 1 -pentanol, or 2 -propanol(b) chlorocyclohexane, cyclohexanol, or 1,2 -cyclohexanediol(c) phenol, cyclohexanol, or 4 -methylcyclohexanol
Predict which member of each group is most soluble in water, and explain the reasons for your predictions. (a) 1 -butanol, 1 -pentanol, or 2 -propanol (b) chlorocyclohexane, cyclohexanol, or 1,2 -cyclohexanediol (c) phenol, cyclohexanol, or 4 -methylcyclohexanol...
5 answers
Match the functions 1 through & with one of the functions a through k to form identitiescos(e) sinco)tan(9)cot(0)Fnaacsc(0)sin? '(0)simg( Cos(usec(0)cos(0cos? (0)cos?(0)cos((cos?(0) + sin? (0)sin(osin" (0)sing0)seccos(0)
Match the functions 1 through & with one of the functions a through k to form identities cos(e) sinco) tan(9) cot(0) Fnaa csc(0) sin? '(0) simg( Cos(u sec(0) cos(0 cos? (0) cos?(0) cos(( cos?(0) + sin? (0) sin(o sin" (0) sing0) sec cos(0)...
5 answers
[8 Points] What are the quotient and remainder when 25 is divided by 42 0 is divided by 172 -10 is divided by 11? 2 is divided by 10
[8 Points] What are the quotient and remainder when 25 is divided by 42 0 is divided by 172 -10 is divided by 11? 2 is divided by 10...
5 answers
If cos €and CSC x < 0, then find exact values for each of thesesin 21cos 2ctan 2x
If cos € and CSC x < 0, then find exact values for each of these sin 21 cos 2c tan 2x...
1 answers
Use the inverses found in Problems $31-40$ to solve each system of equations. $$\left\{\begin{aligned} -4 x+y &=0 \\ 6 x-2 y &=14 \end{aligned}\right.$$
use the inverses found in Problems $31-40$ to solve each system of equations. $$\left\{\begin{aligned} -4 x+y &=0 \\ 6 x-2 y &=14 \end{aligned}\right.$$...
5 answers
Q16. What is the net work Ws,net Ws,12 + Ws,23 + Ws,34 + Ws,4I done by the gas during the entire cycle?Ws,net 1550 J Ws,net ~ 234J Ws,net ~ 577 J Ws,net ~ 948 J Ws,net ~ 300 J
Q16. What is the net work Ws,net Ws,12 + Ws,23 + Ws,34 + Ws,4I done by the gas during the entire cycle? Ws,net 1550 J Ws,net ~ 234J Ws,net ~ 577 J Ws,net ~ 948 J Ws,net ~ 300 J...
5 answers
Number of individuals with each genotype Population Population 2 Population 3 30Population 4 36Homozygous dominant Heterozygous36Homozygous recessive22
Number of individuals with each genotype Population Population 2 Population 3 30 Population 4 36 Homozygous dominant Heterozygous 36 Homozygous recessive 22...
5 answers
(1 point) What are the rectangular coordinates of the point whose cylindrical coordinates are 6, 0 0.6,
(1 point) What are the rectangular coordinates of the point whose cylindrical coordinates are 6, 0 0.6,...

-- 0.021564--