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Sagot :
Answer:
Explanation:
Initially no of atoms of A = N₀(A)
Initially no of atoms of B = N₀(B)
5 X N₀(A) = N₀(B)
N = N₀ [tex]e^{-\lambda t}[/tex]
N is no of atoms after time t , λ is decay constant and t is time .
For A
N(A) = N(A)₀ [tex]e^{-\lambda_1 t}[/tex]
For B
N(B) = N(B)₀ [tex]e^{-\lambda_2 t}[/tex]
N(A) = N(B) , for t = 2 h
N(A)₀ [tex]e^{-\lambda_1 t}[/tex] = N(B)₀ [tex]e^{-\lambda_2 t}[/tex]
N(A)₀ [tex]e^{-\lambda_1 t}[/tex] = 5 x N₀(A) [tex]e^{-\lambda_2 t}[/tex]
[tex]e^{-\lambda_1 t}[/tex] = 5 [tex]e^{-\lambda_2 t}[/tex]
[tex]e^{\lambda_2 t}[/tex] = 5 [tex]e^{\lambda_1 t}[/tex]
half life = .693 / λ
For A
.77 = .693 / λ₁
λ₁ = .9 h⁻¹
[tex]e^{\lambda_2 t}[/tex] = 5 [tex]e^{\lambda_1 t}[/tex]
Putting t = 2 h , λ₁ = .9 h⁻¹
[tex]e^{\lambda_2\times 2}[/tex] = 5 [tex]e^{.9\times 2}[/tex]
[tex]e^{\lambda_2\times 2}[/tex] = 30.25
2 x λ₂ = 3.41
λ₂ = 1.7047
Half life of B = .693 / 1.7047
= .4065 hours .
= .41 hours .
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