How Many Daughter Nuclei Exist at Equilibrium in Radioactive Disintegration?

[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=N_o (because its at equilibrium)
→e^-tλ=1
tλ=0??

 

[clamtrox]

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?

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=N_o (because its at equilibrium)
→e^-tλ=1
tλ=0??

 

[Hysteria X]

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?

 

[clamtrox]

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

 

[paranormal]

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.