Element X is a radioactive isotope such that every 16 years, its mass decreases by half. Given that the initial mass of a sample of Element X is 5900 grams, how much of the element would remain after 27 years,to the nearest whole number?

Question

Element X is a radioactive isotope such that every 16 years, its mass decreases by half. Given that the initial mass of a sample of Element X is 5900 grams, how much of the element would remain after 27 years,to the nearest whole number?

Answer 1

### 1840 grams

Answer 2

## Step 1: Determine the number of half-lives### Divide the total time elapsed (27 years) by the half-life duration (16 years) to calculate how many half-lives have passed:

This means 1 full half-life has passed, and a fraction of another half-life remains.## Step 2: Apply the decay formula### Use the radioactive decay formula:

where:-

grams (initial mass),-

(number of half-lives).Substitute the values:

## Step 3: Simplify the calculation### Compute the value of \(\left(\frac{1}{2}\right)^{1.6875}\):

Now multiply:

## Step 4: Round to the nearest whole number### The remaining mass is approximately

grams after rounding.

Question

Element X is a radioactive isotope such that every 16 years, its mass decreases by half. Given that the initial mass of a sample of Element X is 5900 grams, how much of the element would remain after 27 years,to the nearest whole number?

Solution

Answer

Explanation