Answer: The amount of element X remain after 40 years is 18.75 grams
Explanation:
We are given:
Total time period = 40 years
One half life = 10 years
Calculating the number of half lives, [tex]n=\frac{\text{Total time period}}{\text{One half life}}[/tex]
[tex]n=\frac{40}{10}=4[/tex]
To calculate the amount of element X after 4 half lives, we use the equation:
[tex]a=\frac{a_o}{2^n}[/tex]
where,
a = amount of X after n-half lives
[tex]a_o[/tex] = initial amount of X = 300 g
n = number of half lives = 4
Putting values in above equation, we get:
[tex]a=\frac{300}{2^4}\\\\a=18.75g[/tex]
Hence, the amount of element X remain after 40 years is 18.75 grams
