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Thc radioactivc isolopt p) hall-life 0f 2.86 days. sample containing this isotope initial activity at ([ 0) 0f4.50 X10 By: Calculatc te numbcr Of puclci that will d...

Question

Thc radioactivc isolopt p) hall-life 0f 2.86 days. sample containing this isotope initial activity at ([ 0) 0f4.50 X10 By: Calculatc te numbcr Of puclci that will decay in thc time interval berween 61 30,0 hours aud I2 ' 60.0 hours. nuclei

Thc radioactivc isolopt p) hall-life 0f 2.86 days. sample containing this isotope initial activity at ([ 0) 0f4.50 X10 By: Calculatc te numbcr Of puclci that will decay in thc time interval berween 61 30,0 hours aud I2 ' 60.0 hours. nuclei



Answers

The radioactive isotope $^{198}$ Au has a half-life of 64.8 h. A sample containing this isotope has an initial activity $(t=0)$ of $40.0 \mu$ Ci. Calculate the number of nuclei that decay in the time interval between $t_{1}=10.0 \mathrm{h}$ and $t_{2}=12.0 \mathrm{h}$

Uh, using the concept off half life period off the radioactive substances in terms of decay constant and knowing the value value off initial radio activity off 1 98 you isotope weaken didn't mind the number of nuclear that they decay and they're given developed time. So the number of nuclei and one and 22 and one that the case in the interval between the time, um, to a 92 off the radioactive sample 1 98. You is computed by using the formula, and to two. And one is a girl too. Are not behalf A bond 0.6 93 b to the power minus a 0.693 up on behalf they to minus a to the power minus 0.693 upon behalf Day one. Um, here have life period off 19. So 1 98 au is and the initial radio activity off when I did a u isotope is are not so ah, half life off the radioactive isotope, Um, 1 19 a U. S. 64.8 hours. Um, there is equal. That is 2.33280 in tow. Tend to the power five seconds and the initial radio activity off. 1 98. You is 40 Micros EI. That is equal to 1.48 in 10 to the power six. The case four second and the number of nuclei that became that I'm intervals between the times. Um, t one is 10 hour and two is 12 hours. So, um um but the formula for high fly spirit off the radioactive substances in terms off decay constant. Lambda is given by t half is 0.693 upon Lambda. So, lambda is there a 0.693 upon p half. So, um, we have, um 693 upon t half is 2.3 3 to 18 to 10 to the power. Five seconds. So lambda is there a point to 97 into 10 to deeper, minus five per second. And we know the form. Love for the number of nuclear that decay. In the interval between the times t one and T to work the radio active sample I won 98 au is and to Penis and one is are not behalf Upon 0.693 multiplied by eight to the power minus 0.693 or four. Behalf multiplied by 81 32 minus a to the power 0.693 upon t half multiplied by 81 on for N one minus and two is are not upon multiplied by a half upon 3.693 a to the power 0.693 upon t half Do you want minus e to the power minus 0.693 20 half ti toa eso From this we have, uh, by putting the values off are not anti half. We will get the value as, um nine 0.47 and to tend to the power ninth nuclear. So the number of nuclei therefore the number off nuclear that decay in the time period in the given interval off time defense upon half life period, then initial radio activity Radio at PVT off the the directive substances and time in true

To find he number off. You cry. Ah, beauty Fullback on using the activity since the activities related to the normal UK fire d decay constant. So over here we want to find What is he towards animals. In fact, that Kate, between some time interval, right, we didn't $10.12 hours. So all you need is t activity at $10 activity at Joe Flowers. And from there you can find what is the change de and failure. So right now, to fight audience activities, we will first need to use the decay law. Right? Reduced the activity to the initial activity. In fact, he not which is given this 40 micro curies. Let the backs would ensure negative. The t so lambda, in this case you take a constant is given a slot to off t half 64.8. So substituting that in Mississippi Pretty Michael. Curious what? Bye bye, Exponent. Show teeth on to 10/64. Point it. I saw the r U C unit step off in hours so they can sew it. Shut out! You got to do the same process for the Jeff. Always one. Okay, this is just 40. Michael. Curious Ensured. Already flown to show off 64 point it. Remember that this also equals two Lunda times. The number off do you cry? Shop hours this week goes to the I don't see number on your case. 10 of us. So in order to find the difference, right? The difference in the nobody, right? They will give us the noble. You got that, Kate, right? You just have to find we take each off o e 10 minus itself. You gotta buy Linda. Circular City number off the case that I could between these time, period. All right. And with this, in order to get the actual inability case, you have a convert. I'll listen to seconds. Michael Curie's in two back Gross. So 40 Michael Curie's You can call my debt by multiplying by 10 po off. Wait. Us six took over for Michael. Curious too Curious. In a multiplied by 3.7 times Sent Po of 10. It's number. Bekoe spoke Yuri for you. Always me much by that by treat About 600 seconds. Oh, if every Tatis expression final answer would be 9.47 posted above night

To find the decay constant. We simply need to use the first order, integrated rate law and any two sets of data points in the table that's given to us. We'll use the 1st 2 activity after one day is three 189 and activity on time zero day day zero is 500. That's going to be equal. The negative k, which we are attempting to calculate, replied. By the time that has elapsed with its one day So we saw for Cain, we get 0.251 one over days and then calculate the half life by taking McKay and dividing it into the natural log of two, and we have 2.76 days.

Here we could defer Mullah Nature Log and D are in Not is it well toe minus Linda de and have lives? Is it well too? 0.693 our Glenda from decay zero toe day one from the gay zero toe day one day one nature log Cree age nine Oh, learn 500 is equal to Linda One day them days it will too. 0.251 But dear lived ledge find encouragement. You off Linda It we're yes, dime more de must Linda 30 dying zero must he's 500 dying one Mars 3 89 Time Do must trees in a tree dying t mas so praecis during food must one and for dying playoff must one for cree time six must 112 is Iran boy do by one 0.2 50 times It'll blind no 50 0.2 50 zero boy into 50 zero point for nine. Yeah, every limb The average music will toe zero going toe five party


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