Question

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.

Answer 1

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

Step-by-step explanation:

Given the data in the question;

`T_{(1)/(2)` = ( 4.50 + C ) × 10⁶ years

C = 11

`T_{(1)/(2)` = ( 4.50 + 11 ) × 10⁶ years

`T_{(1)/(2)` = 15.50 × 10⁶ years

`T_{(1)/(2)` = 15.50 × 10⁶ × 365 × 24 × 60 × 60

λ = 0.693 /
`T_{(1)/(2)`

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