Can someone me with this radiochemistry question please

[shenzys]

Homework Statement

Calculate the radioactive concentration (MBq/ml) of a sodium pertechnetate [99mTC] solution with a concentration of 2.0 * 10^-6 g/L.

Mr (sodium pertechnetate) = 186
half life of [99mTc) = 6.02 hours
Avagadro's constant = 6.02 * 10^23

Homework Equations

A= lamda N
N = mNa/Mr
Moles=mass/Rmm
C=n/v

The Attempt at a Solution

Okay, so the first step would be to work out the decay constant (lamda) from the half life which I can do but, after that I kind of get stuck. Do I need to calculate the activity (A) by using the formula A= lamda N?
How do I work out N if I don't have the mass to work out the moles of the compound? And then how does that enable me to work out the concentration using c=n/v without a volume

Also, am I going about the question the correct way?

 

[nate808]

Yes, you are on the right track with your approach to this problem. Let's break it down step by step:

1. Calculate the decay constant (lamda) using the half-life of [99mTc].
lamda = ln(2) / half-life
= ln(2) / 6.02 hours
= 0.115 hours^-1

2. Use the formula A = lamda N to calculate the activity (A).
Here, N represents the number of atoms present in the sample. We can calculate this using Avogadro's constant and the molar mass of sodium pertechnetate (NaTcO4).
N = (mNa/Mr) * 6.02 * 10^23
= (2.0 * 10^-6 g/L * 1000 mL/L) / 186 g/mol * 6.02 * 10^23
= (2.0 * 10^-3 mol/L) / 186 g/mol * 6.02 * 10^23
= 6.45 * 10^17 atoms/L

Now, we can substitute this value for N in the formula A = lamda N.
A = (0.115 hours^-1) * (6.45 * 10^17 atoms/L)
= 7.43 * 10^16 decays/hour

3. Finally, use the formula C = n/V to calculate the concentration (C) in MBq/mL.
Here, n represents the number of decays per second, which we can calculate by dividing the activity (A) by the number of seconds in an hour (3600 seconds).
n = A / 3600 seconds
= (7.43 * 10^16 decays/hour) / 3600 seconds
= 2.06 * 10^13 decays/second

Now, we can substitute this value for n in the formula C = n/V.
C = (2.06 * 10^13 decays/second) / V
We don't have the volume (V) given in the problem, so we cannot calculate the concentration without that information. However, we can still express the concentration in terms of MBq/mL by converting the units.
C = (2.06 * 10^13 decays/second) / (1 * 10^6 decays

 

[Blueshift5]

Sure, I'd be happy to help with this question. First, let's start by defining some terms and units. MBq/ml stands for megabecquerels per milliliter, which is a unit of radioactive concentration. It measures the number of radioactive decays per second in a given volume. In this case, we are dealing with a sodium pertechnetate solution, which has a concentration of 2.0 * 10^-6 g/L. The Mr (relative molecular mass) of sodium pertechnetate is 186, and its half-life is 6.02 hours. Avagadro's constant is also given as 6.02 * 10^23.

To solve this problem, we need to use the equation A= lamda N, where A is the activity (measured in becquerels), lamda is the decay constant, and N is the number of atoms undergoing radioactive decay. We can calculate lamda using the formula lamda = ln2/t1/2, where t1/2 is the half-life. Plugging in the given half-life of 6.02 hours, we get a decay constant of 0.115 h^-1.

Next, we need to calculate N, which represents the number of atoms in a given mass of the compound. We can do this by first converting the concentration of the solution from g/L to moles/L using the formula moles=mass/Rmm. In this case, the mass is 2.0 * 10^-6 g/L and the Rmm (relative molecular mass) is 186. This gives us a concentration of 1.08 * 10^-8 mol/L.

Now, we can use Avagadro's constant to convert this number of moles to the number of atoms, which is 6.49 * 10^15 atoms/L.

Finally, we can plug in our values for lamda and N into the equation A= lamda N to calculate the activity of the solution. This gives us an activity of 7.46 * 10^14 Bq/L.

To convert this to MBq/ml, we need to divide by 10^6 for the megabecquerel unit and then by 10^-3 for the milliliter unit. This gives us a final answer of 0.746 MBq/ml for the radioactive concentration of the sodium pertechnetate