Question

1. Element X has a mass of 300g and a ½ life of 10 years. How many grams will remain after 40 years? Hint: first determine how many ½ lives there are in 40 years

Answer 1

Answer: The amount of element X remain after 40 years is 18.75 grams

Step-by-step explanation:

We are given:

Total time period = 40 years

One half life = 10 years

Calculating the number of half lives,
`n=\frac{\text{Total time period}}{\text{One half life}}`

`n=(40)/(10)=4`

To calculate the amount of element X after 4 half lives, we use the equation:

`a=(a_o)/(2^n)`

where,

a = amount of X after n-half lives

`a_o` = initial amount of X = 300 g

n = number of half lives = 4

Putting values in above equation, we get:

`a=(300)/(2^4)\\\\a=18.75g`

Hence, the amount of element X remain after 40 years is 18.75 grams