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24Na decays to one-fourth of its initial amount in 29.8 hours. Its decay constant is_________ hour–1 (rounded up to four decimal places).
Correct answer is between '0.0460,0.0470'. Can you explain this answer?
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24Na decays to one-fourth of its initial amount in 29.8 hours. Its dec...
The decay constant (λ) can be determined using the formula:
N(t) = N(0) * e^(-λt)
where N(t) is the amount of the substance at time t, N(0) is the initial amount of the substance, e is the base of the natural logarithm (approximately 2.718), λ is the decay constant, and t is the time.
In this case, we are given that 24Na decays to one-fourth of its initial amount in 29.8 hours. This means that at time t = 29.8 hours, N(t) = N(0)/4.
Substituting these values into the formula, we get:
N(0)/4 = N(0) * e^(-λ * 29.8)
Dividing both sides of the equation by N(0) and rearranging, we have:
1/4 = e^(-λ * 29.8)
Taking the natural logarithm of both sides, we get:
ln(1/4) = -λ * 29.8
Simplifying, we have:
-λ = ln(1/4) / 29.8
Finally, dividing both sides by -1, we find:
λ = -ln(1/4) / 29.8
Evaluating this expression, we find:
λ ≈ 0.0231 hour^-1
Therefore, the decay constant for 24Na is approximately 0.0231 hour^-1.
N(t) = N(0) * e^(-λt)
where N(t) is the amount of the substance at time t, N(0) is the initial amount of the substance, e is the base of the natural logarithm (approximately 2.718), λ is the decay constant, and t is the time.
In this case, we are given that 24Na decays to one-fourth of its initial amount in 29.8 hours. This means that at time t = 29.8 hours, N(t) = N(0)/4.
Substituting these values into the formula, we get:
N(0)/4 = N(0) * e^(-λ * 29.8)
Dividing both sides of the equation by N(0) and rearranging, we have:
1/4 = e^(-λ * 29.8)
Taking the natural logarithm of both sides, we get:
ln(1/4) = -λ * 29.8
Simplifying, we have:
-λ = ln(1/4) / 29.8
Finally, dividing both sides by -1, we find:
λ = -ln(1/4) / 29.8
Evaluating this expression, we find:
λ ≈ 0.0231 hour^-1
Therefore, the decay constant for 24Na is approximately 0.0231 hour^-1.
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24Na decays to one-fourth of its initial amount in 29.8 hours. Its dec...
A0/At=2^n
A0/A0/4=2^n
4=2^n
n=2
n×t1/2=total time
2×t1/2=29.8
t1/2=16.9
dissociation constant =0 .693/16.9. =0.0410
A0/A0/4=2^n
4=2^n
n=2
n×t1/2=total time
2×t1/2=29.8
t1/2=16.9
dissociation constant =0 .693/16.9. =0.0410
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24Na decays to one-fourth of its initial amount in 29.8 hours. Its decay constant is_________ hour–1 (rounded up to four decimal places).Correct answer is between '0.0460,0.0470'. Can you explain this answer?
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