Question

Radium-226, a common isotope of radium, has a half-life of 1,620 years. How many grams of a 120-gram sample will remain after t years? which equation can you use to solve this problem? mc001-1. Jpg mc001-2. Jpg mc001-3. Jpg.

Answer 1

The amount of a radioactive isotope remaining after some time is calculated using the half-life formula, with Radium-226's half-life of 1,620 years and the initial sample mass factored into the equation.

Step-by-step explanation:

To calculate the remaining amount of a radioactive isotope after a certain period, we use the half-life formula. For Radium-226 with a half-life of 1,620 years, the decay formula is:

N = N0 × (1/2)^(t/t₁/₂)

where N is the final amount of the isotope, N0 is the initial amount, t is the time that has elapsed, and t₁/₂ is the half-life of the isotope. In the question with a 120-gram sample, we can plug these values into the formula to find the amount remaining after t years.

Answer 2

The equation that can be used to solve this problem is Final amount = Initial amount * (0.5)^(t/h), where 'Final amount' represents the amount of the sample remaining after time 't', 'Initial amount' represents the initial amount of the sample, 't' represents the time in years, and 'h' represents the half-life of the isotope.

Step-by-step explanation:

To solve this problem, we can use the equation: Final amount = Initial amount * (0.5)^(t/h), where 'Final amount' represents the amount of the sample remaining after time 't', 'Initial amount' represents the initial amount of the sample, 't' represents the time in years, and 'h' represents the half-life of the isotope.

Using the given information, we know that the initial amount is 120 grams and the half-life is 1,620 years. So, the equation becomes: Final amount = 120 * (0.5)^(t/1620).

Substitute the values given in the equation and solve for 'Final amount'. This will give you the number of grams remaining after 't' years.