How Many Daughter Nuclei Exist at Equilibrium in Radioactive Disintegration?

• Hysteria X
In summary, the half-lives of the parent and daughter nuclides in a chain radioactive disintegration are 10 years and 25 years, respectively. At equilibrium, with the parent number of nuclei at 5*10^8, the number of daughter nuclei will also be 5*10^8. The equation for this condition is n=n0, where n0 is the initial number of parent nuclei and n is the final number of daughter nuclei.
Hysteria X

Homework Statement

In a chain radioactive disintegration,the half-life of the parent and daughter nuclide are 10 years and 25 years respectively.if the disintegration process is at its equilibrium stage with the parent no. of nuclei equal to 5* 10^8, the daughter no. of nuclei will be

Homework Equations

t1/2 = 0.639/λ

n/n0=(1/2)^(t/(t1/2))

n/n0=##e^-λt##

The Attempt at a Solution

t11/2 = 10 years
t21/2 = 25 years
N=No (because its at equilibrium)
→e^-tλ=1
tλ=0??

I would imagine that the processes being in equilibrium means that the number of daughter nuclei that decay is equal to the number of parent nuclei that decay. Can you write an equation from this condition?

Hysteria X said:

Homework Statement

In a chain radioactive disintegration,the half-life of the parent and daughter nuclide are 10 years and 25 years respectively.if the disintegration process is at its equilibrium stage with the parent no. of nuclei equal to 5* 10^8, the daughter no. of nuclei will be

Homework Equations

t1/2 = 0.639/λ

n/n0=(1/2)^(t/(t1/2))

n/n0=##e^-λt##

The Attempt at a Solution

t11/2 = 10 years
t21/2 = 25 years
N=No (because its at equilibrium)
→e^-tλ=1
tλ=0??

yes that's what i have writtern n=n0 ?? initial number of nucleus ie parent nuclei = n0 and final number of nuclei ie daughter nuclei=n?
or should i take all together two different equations?

No, that's not correct. What's the number of nuclei that decay in a given time?

The problem states that the disintegration process is at its equilibrium stage, meaning that the rate of decay of the parent nuclei is equal to the rate of production of daughter nuclei. Therefore, we can use the equation n/n0=##e^-λt## to find the daughter nuclei at equilibrium.

Substituting the given values, we get:

n/n0=##e^-tλ##
= ##e^-t/(10 years)##
= ##e^-t/(10*365*24*60*60 seconds)##

Since we are looking for the number of daughter nuclei when the parent nuclei is 5*10^8, we can set up the equation as:

5*10^8 = ##e^-t/(10*365*24*60*60 seconds)##

Solving for t, we get:

t = ln(5*10^8) * 10*365*24*60*60 seconds
= 1.609*10^10 seconds

Therefore, at equilibrium, the number of daughter nuclei will also be 5*10^8.

What is "A Disintegration Problem"?

"A Disintegration Problem" is a scientific phenomenon where a substance breaks down into smaller components, either by physical or chemical means, resulting in a change in its properties or structure.

What causes a disintegration problem to occur?

A disintegration problem can be caused by various factors such as exposure to heat, light, moisture, or chemical reactions. It can also occur naturally over time due to decay or decomposition.

How does disintegration affect the properties of a substance?

The disintegration of a substance can alter its physical and chemical properties, such as color, texture, density, or chemical composition. This can lead to changes in its functionality or effectiveness.

What are the potential consequences of a disintegration problem?

A disintegration problem can have both positive and negative consequences. It can be beneficial in some cases, such as the breakdown of waste or the decomposition of organic matter. However, it can also be harmful, causing damage to structures, products, or the environment.

How can scientists prevent or control a disintegration problem?

Scientists can prevent or control a disintegration problem by understanding the cause and implementing measures to mitigate it. This can include storing substances in controlled environments, using protective coatings, or conducting regular maintenance and testing.

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