Respuesta :
Answer:
how many would remain
after one half-life = 200 atoms
After 2 half-lives = 100 atoms
After 3 half-lives = 50 atoms
After 4 half-lives = 25 atoms
Explanation:
Given;
Initial amount = 400 atoms
Half life is the time taken to decay half of a radioactive material.
how many would remain after one half-life;
= 400/2 = 200 atoms
After 2 half-lives;
= 400/2^2 = 400/4
= 100 atoms
After 3 half-lives
= 400/2^3 = 400/8
= 50 atoms
After 4 half-lives
= 400/2^4 = 400/16
= 25 atoms
The half-life is the time it takes the number of atoms to remain half of the
initial number of atoms.
- Number of atoms remaining after 2 half lives are 100 atoms
- Number of atoms remaining after 3 half lives are 50 atoms
- Number of atoms remaining after 4 half lives are 25 atoms
Reasons:
The initial number of radioactive atoms, N₀ = 400
Required:
The number of atoms that will remain after 2 half lives?
Solution:
Half life is given by the formula;
[tex]N(t) = N_0 \left (\dfrac{1}{2} \right )^{\dfrac{t}{t_{1/2}}[/tex]
After 2 half lives, we have;
t = 2 × [tex]t_{1/2}[/tex]
Which gives;
[tex]N(2 \times t_{1/2}) = 400 \times \left (\dfrac{1}{2} \right )^{\dfrac{2 \times t_{1/2}}{t_{1/2}}} = 400 \times \left (\dfrac{1}{2} \right )^2 = 100[/tex]
The number of atoms remaining after 2 half lives = 100
After 3 half-lives, we have;
[tex]N(3 \times t_{1/2}) = 400 \times \left (\dfrac{1}{2} \right )^{\dfrac{3 \times t_{1/2}}{t_{1/2}}} = 400 \times \left (\dfrac{1}{2} \right )^3 = 50[/tex]
The number of atoms remaining after 3 half lives = 50
After 4 half-lives, we have:
[tex]N(4 \times t_{1/2}) = \mathbf{400 \times \left (\dfrac{1}{2} \right )^{\dfrac{4 \times t_{1/2}}{t_{1/2}}}} = 400 \times \left (\dfrac{1}{2} \right )^4 = 25[/tex]
The number of atoms remaining after 4 half lives = 25
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