The half life of an element Z is 10days. if there are 10g of Z intially, what will be its mass after 40 days?
four half-lives ... 10 g * (1/2)^(40 / 10)
30g
To calculate the mass of the element Z after a certain time, we need to understand the concept of half-life. The half-life of an element is the time it takes for half of the substance to decay or transform into another element.
In this case, the half-life of element Z is given as 10 days. This means that after 10 days, half of the initial amount will remain, and after another 10 days, half of the remaining amount will remain, and so on.
Now, let's calculate the mass of element Z after 40 days:
1. First, we need to determine how many half-lives have passed in 40 days. Since the half-life of element Z is 10 days, we divide 40 by 10 to find the number of half-lives: 40/10 = 4 half-lives.
2. Each half-life reduces the mass by half. So, after 4 half-lives, the remaining mass will be (1/2) ^ 4 of the initial mass.
(1/2) ^ 4 = 1/16
This means that after 4 half-lives, only 1/16th of the initial mass will remain.
3. Finally, we calculate the remaining mass of element Z:
Remaining mass = Initial mass × (1/2) ^ Number of half-lives
Remaining mass = 10g × (1/2) ^ 4
= 10g × (1/16)
= 10g/16
= 0.625g
Therefore, after 40 days, the mass of element Z will be 0.625 grams.