Final answer:
To find the number of years it takes for 50 mg of radium-226 to decay, divide the initial amount by 2 repeatedly until you reach 50 mg, then multiply the number of divisions by the half-life of radium-226.
Step-by-step explanation:
To find the number of years it takes for 50 mg of radium-226 to decay, we need to use the concept of half-life. The half-life of radium-226 is 1590 years, which means that in 1590 years, half of the original amount of radium-226 will decay. Start with the initial amount of radium-226, 100 mg, and divide it by 2 repeatedly until you reach 50 mg. Count the number of divisions, and multiply that by 1590 years to find the time it takes for the amount to decrease to 50 mg. Let's work through the steps:
- Starting with 100 mg, divide by 2: 100 mg ÷ 2 = 50 mg
- It took 1 division to reach 50 mg. Multiply 1 by 1590 years to find the time it took: 1 × 1590 years = 1590 years
Therefore, it will take 1590 years for 50 mg of radium-226 to remain.