Respuesta :
the element would remain after 25 years is 2,325 grams !
Step-by-step explanation:
Here we have , Element X is a radioactive isotope such that every 13 years, its mass decreases by half. Given that the initial mass of a sample of Element X is 8800 grams, We need to find how much of the element would remain after 25 years . Let's find out:
According to question , Element X is a radioactive isotope such that every 13 years, its mass decreases by half , And initial mass of a sample of Element X is 8800 grams . So , following equation will be framed for the mass of sample X after t years as :
⇒ [tex]M = 8800(\frac{1}{2} )^\frac{t}{13}[/tex]
⇒ [tex]M = 8800(0.5 )^\frac{t}{13}[/tex]
Now , the mass of element after 25 years is given by :
⇒ [tex]M = 8800(0.5 )^\frac{25}{13}[/tex]
⇒ [tex]M = 8800(0.26)[/tex]
⇒ [tex]M = 2,325g[/tex]
Therefore , the element would remain after 25 years is 2,325 grams !
