# How Many 116In Nuclei Can Be in Equilibrium?

• Apollo14LMP
In summary: You seem to be having exactly the same problems here, but you are just using different numbers.In summary, the problem is to calculate the maximum number of 116In nuclei in equilibrium in a sample given that the rate of production of 116In nuclei is 10 per second and the half-life of 116In is 54 minutes (converted to seconds as 3240 seconds). Using the equation (In2)/λ = (In2)/3240, the value of λ can be found to be 2.14 x 10^-4 s^-1. Then using the equation A = R - λN(t), where A is the activity, R is the rate of production, and N(t) is the number of nuclei
Apollo14LMP

## Homework Statement

Can someone check this please ?

Calculate the maximum number of 116In nuclei (number in equilibrium) in the sample if the half-life of 116In is 54 m.

## The Attempt at a Solution

The half life is 54 minutes, converted to seconds = 54m x 60 s-1 = 3.24 x 10^3 s-1

(In2) / λ = In2 / 3.24 x 10^3 s-1 = 2.14 x 10^-4 s-1

A = R - λN(t) So, A = 10 s-1 / 2.14 x 10^-4 s-1= 4.67×10^4 nuclei

The number of nuclei in the sample N = mNA/A, where is the fraction of the isotope (atomic mass A) in the sample (mass m) and NA is Avogadro's number.

N = 4.67×10^4 x 6.022^23 / 116 = 2.42 x 10^26 s-1 Equilibrium activity = 2.42 x 10^26 s-1

## Homework Statement

That sure does not look like the entire problem statement. There seems to be an implied production of 116In that you have not explained.

There are 60 seconds per minute. Your notation is weird. You seem to be getting inverse seconds instead of seconds for the seconds equivalent to 54 minutes.

Can't figure out what the various things in A = R - λN(t) mean. Can't figure out how that has anything to do with the rest of that line, since you don't subtract anything from anything. Does not look like you have calculated λ, just used an equation it appears in, so the substitution is confusing.

That's enough places where you are very sloppy. I'm stopping. Maybe you could start over and be more careful?

1 person
In the capture reaction 115In + n 116In, 116In nuclei are produced at the rate of 10 s-1. Calculate the maximum number of 116In nuclei (number in equilibrium) in the sample if the half-life of 116In is 54 m.

The half life is 54 minutes, converted to seconds = 54m x 60 s-1 = 3240 s-1

(In2) / λ = In2 / 3240 s-1 = 2.14 x 10^-4 s-1

So, 10s-1 / 2.14 x 10^-4 s-1 = 4.67×10^4 nuclei

The number of nuclei in the sample N = mNA/A, where the fraction of the isotope (atomic mass is A) in the sample (mass m) and NA is Avogadro's number.

N = 4.67×10^4 x 6.022 x 10^23 / 116 = 2.42 x 10^26 s-1

Equilibrium activity = 2.42 x 10^26 s-1

Last edited:
Perhaps you didn't get DE's message; if you don't want to tell, that's fine. In the mean time you leave me wondering what you mean with N=mNA/A. Was m a given ? then why not tell us, especially after DE explicitly asks for the entire problem statement ? But I suspect m is not a given, because it's irrelevant.

How can you write N = ... s-1 ? Is s-1 the dimension of a number ?

Why care about N at all if you were given that the 116In nuclei are produced at the rate of 10 s-1 ?

What on Earth is In2 ? Never heard of that isotope !Please spend some time reading the guidelines and the tips and what have you, so you can write s-1 if that is what you mean with "per second" (which is NOT, repeat NOT the dimension of a half-life).

Oh, and: did you notice all your relevant equations have disappeared as if by magic ? No wonder there's nothing sensible coming out ! Please spend some time collecting and rendering the relevant equations.

This isn't meant as bashing, but really: if you want someone to help you (and there really are people about who do), you shouldn't make it impossible for them !

So start over with this simple exercise: there are ten 116In nuclei that get produced per second. If there are N 116In nuclei present, the number that decay per second is something like N/##\tau##. So by the time N/##\tau## = 10 s-1 just as many decay as there are being formed. What can be easier ?

The problem is in all aspects (apart from actual numbers and that we are here solving for a different quantity) equivalent to your earlier thread
Why don't you go back and review that thread rather than starting a new one on the same subject? The replies you will get are going to be saying essentially the same as what I said there. Your main problem in that thread seemed to be interpreting what different terms were actually representing as well as unit analysis when adding different quantities.

## 1. What is radioactive decay?

Radioactive decay is the process by which an unstable atomic nucleus spontaneously breaks down, releasing energy and forming a different, more stable nucleus.

## 2. How does radioactive decay occur?

Radioactive decay occurs when the strong nuclear force holding the nucleus together is not strong enough to overcome the electrostatic repulsion between the positively charged protons. This causes the nucleus to emit radiation and undergo a transformation into a more stable configuration.

## 3. What is the half-life of a radioactive substance?

The half-life of a radioactive substance is the amount of time it takes for half of the original amount of the substance to decay. This is a constant value for each radioactive element and is used to measure the rate of decay.

## 4. How is radioactive decay measured?

Radioactive decay is measured using a unit called the Becquerel (Bq), which represents one decay per second. Another commonly used unit is the Curie (Ci), which is equal to 3.7 x 10^10 Bq.

## 5. What is the significance of radioactive decay in science?

Radioactive decay is important in many fields of science, including medicine, energy production, and geology. It allows us to accurately date rocks and fossils, diagnose and treat diseases, and generate electricity through nuclear reactions.

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