Okay so I have this assignment and I thought I knew how to do this but appearntly I am just lost. I know what the answer is suposed to be and I am deifantly no wheres near that. If you can sorta point me in the right direction that would be great. Thanks! The question is:
The isotope 99mTc, (t ½ = 6.01 hours) is used in the diagnostic imaging of the heart and other organs. For diagnosing heart function, a particular dose has an activity of 3.09 x 108 disintegrations per second. Calculate the mass in grams of 99mTc required to produce this activity level. Use 98.91 amu as the atomic mass of 99mTc.
I thought you would use A=landaN and solve for N. And then you woudl get landa by using landa=0.693/(t1/2) and then just divide the amount for N by avagadros number to get moles, then change the moles to grams. Then chnage the mass they give you to grams and multiply the moles that you found for N by the gram amount and you would get the mass. I don't know if that makes sense but it does on my paper.
Use Activity= lambda*N Yes, lambda is .693/t1/2. Yes, you proceeded correctly, get moles, then grams.
N/avonumber * 98.91 = mass you are looking for.
But that doesnt work out cause that's what I did. But you still need to chnage to grams, and when you do it is WAYYYY wrong. lol I'm so confused
let me see your calcs.
Okay:
A= 3.09 X10^8 dis./s
t1/2= 6.01hrs
A=landaN
N=A/landa
Units are in seconds so gotta chnage the t1/2 to seconds
Landa=(0.693/6.01hrs)(1hr/60min)(1min/60s)
=0.00003203 /s
N=(3.09 x 10^8 dis/s)/(0.00003203 /s)
= 9.647205745 x 10^12 N
9.647205745 x 10^12N(1mol/6.022 x 10^23)
= 1.601993647 x 10^-11mol
98.91amu(1.66054 x 10^-24g /1amu)
= 1.642440114 x 10^-22g
= 1.601993647 x 10^-11mol (1.642440114 x 10^-22g /1mol)
=2.63 x 10^-33g
The answer is supposed to be 1.58 x10^-9g
Okay:
A= 3.09 X10^8 dis./s
t1/2= 6.01hrs
A=landaN
N=A/landa
Units are in seconds so gotta chnage the t1/2 to seconds
Landa=(0.693/6.01hrs)(1hr/60min)(1min/60s)
=0.00003203 /s
N=(3.09 x 10^8 dis/s)/(0.00003203 /s)
= 9.647205745 x 10^12 N
9.647205745 x 10^12N(1mol/6.022 x 10^23)
= 1.601993647 x 10^-11mol
<font=14>You are OK to here. Now just multiply 1.602 x 10^-11 x 98.91 = 1,58 x 10^-9 g</font=12>
98.91amu(1.66054 x 10^-24g /1amu)
= 1.642440114 x 10^-22g
= 1.601993647 x 10^-11mol (1.642440114 x 10^-22g /1mol)
=2.63 x 10^-33g
The answer is supposed to be 1.58 x10^-9g
N/avonumber * 98.91 = mass you are looking for.
But N= A/lambda= A*t1/2/.693
Now t1/2 has to be in seconds...
N= 3.09E8*6.01hr*3600sec/hr /.693
N= 9.65E12
mass= N/avonumber * 98.91
=9.65E12*98.91/6.02E23
=1.59 nanograms
check that.
Ohhh okay. so I think what I was doing wrong was just the fact that I was changing the AMU to grams, then dividing it and I forgot that amu can be considered grams at some points/
Okay thanks, I think I got it. I got 2.0E-9 so at least I know I'm in the right area. Thanks sooooo much.
I went through this independently and obtained 1.58 x 10^-9 g, also.
You're welcome! I'm glad I could help. It seems like the issue was that you were converting the atomic mass unit (amu) to grams before dividing by Avogadro's number. However, amu can be considered as grams in this context, so you can directly multiply the number of moles (N) by the atomic mass (98.91 amu) to get the mass in grams.
Just to clarify, the correct calculation is:
N = A * t1/2 / 0.693
where A is the activity (3.09 x 10^8 disintegrations per second) and t1/2 is the half-life (6.01 hours converted to seconds).
Then, mass = N / Avogadro's number * atomic mass
Plugging in the values, you should get a mass of 1.58 x 10^-9 grams.
If you have any more questions, feel free to ask!