This question is incomplete, the complete question is;
g Consider a pure sample of a radioactive isotope with a mass number of (46 + A). If the sample has mass of (25.0 + B) micrograms and the isotope has a half-life of (4.50 + C)x10⁶ years,
determine the decay rate for the sample. Give your answer in decays/second and with 3 significant figures.
A = 1, B = 1, C = 11.
Answer:
the decay rate for the sample is 469,625.898 decay/s
Explanation:
Given the data in the question;
[tex]T_{\frac{1}{2}[/tex] = ( 4.50 + C ) × 10⁶ years
C = 11
[tex]T_{\frac{1}{2}[/tex] = ( 4.50 + 11 ) × 10⁶ years
[tex]T_{\frac{1}{2}[/tex] = 15.50 × 10⁶ years
[tex]T_{\frac{1}{2}[/tex] = 15.50 × 10⁶ × 365 × 24 × 60 × 60
λ = 0.693 / [tex]T_{\frac{1}{2}[/tex]
so
λ = 0.693 / ( 15.50 × 10⁶ × 365 × 24 × 60 × 60 )
also
N = ( 25.0 + B )
B = 1
N = ( 25.0 + 1 )
N = 26 × 10⁻⁶
isotope with a mass number of ( 46.0 + A ) , A=1
= ( 46.0 + 1 ) = 47
N = 26 × 10⁻⁶( 1/47 )( 1 / 1.67 × 10⁻²⁷ ) = 3.31252 × 10²⁰
R = λN
so
R = (0.693 / ( 15.50 × 10⁶ × 365 × 24 × 60 × 60 )) × (3.31252 × 10²⁰)
R = 1.41773 × 10⁻¹⁵ × (3.31252 × 10²⁰)
R = 469,625.898 decay/s
Therefore, the decay rate for the sample is 469,625.898 decay/s
