Respuesta :
Answer:
5.8μg
Explanation:
According to the rate or decay law:
N/N₀ = exp(-λt)------------------------------- (1)
Where N = Current quantity, μg
N₀ = Original quantity, μg
λ= Decay constant day⁻¹
t = time in days
Since the half life is 4.5 days, we can calculate the λ from (1) by substituting N/N₀ = 0.5
0.5 = exp (-4.5λ)
ln 0.5 = -4.5λ
-0.6931 = -4.5λ
λ = -0.6931 /-4.5
=0.1540 day⁻¹
Substituting into (1) we have :
N/N₀ = exp(-0.154t)----------------------------- (2)
To receive 5.0 μg of the nuclide with a delivery time of 24 hours or 1 day:
N = 5.0 μg
N₀ = Unknown
t = 1 day
Substituting into (2) we have
[5/N₀] = exp (-0.154 x 1)
5/N₀ = 0.8572
N₀ = 5/0.8572
= 5.8329μg
≈ 5.8μg
The Chemist must order 5.8μg of 47-CaCO3
"When The Chemist must order 5.8μg of 47-CaCO3 = 5.8μg To understand more information check below".
What is Decay law?
Now, According to the rate of decay law:
Then, N/N₀ is = [tex]exp(-\lambda)[/tex]-------------------eq. (1)
Where N is = Current quantity, μg
N₀ is = Original quantity, μg
Then, λ= Decay constant day⁻¹
After that, t is = the time days
When the half-life is 4.5 days, Then, we can compute the λ from (1) by substituting N/N₀ = 0.5
Then, 0.5 is = exp (-4.5λ)
After that, ln 0.5 = -4.5λ
Now, -0.6931 is = -4.5λ
Then, λ = -0.6931 /-4.5
After that, =0.1540 days⁻¹
Now, Then Substituting into (1) we have :
Then, N/N₀ is =[tex]exp(-0.154t)[/tex]--------------eq. (2)
After that, To receive 5.0 μg of the nuclide with a delivery time of 24 hours or 1 day:
N is = 5.0 μg
Then, N₀ is = Unknown
After that, t is = 1 day
Then, Substituting into (2) we have
After that,[tex][5/N₀] = exp (-0.154 x 1)[/tex]
Now, 5/N₀ = 0.8572
Then, N₀ = 5/0.8572
Now, = 5.8329μg
Hence, ≈ 5.8μg
Thus, The Chemist must order 5.8μg of [tex]47-CaCO3[/tex]
Find more information about Decay law here:
https://brainly.com/question/9902363
