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The table shows the amount of radioactive element remaining in a sample over a period of time. radioactive decay rate amount of radioactive sample (grams) time (years) 56.0 0 47.1 400 39.6 800 33.3 1,200 28 1,600 part 1: what is the half-life of the element? explain how you determined this. part 2: how long would it take 312 g of the sample to decay to 9.75 grams? show your work or explain your answer.

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Eduard22sly

1. The half life of the element, given the data from the question is 1600 years

2. The time taken for 312 g of the sample to decay to 9.75 grams is 8000 years

1. How to determine the half life of the element

Half-life is the time taken for half a material to decay.

To determine the half life of the given element, do the following:

  • Original amount = 56 g
  • Half the original amount = 56 / 2 = 28 g
  • Time for 28 g = 1600 year
  • Half life of element = 1600 years

How to determine the time

We'll begin by determining the number of half-lives that has elapsed. This can be obtained as follow:

  • Original amount (N₀) = 312 g
  • Amount remaining (N) = 9.75 g
  • Number of half-lives (n) =?

2ⁿ = N₀ / N

2ⁿ = 312 / 9.75

2ⁿ = 32

2ⁿ = 2⁵

n = 5

Finally, we shall determine the time. This can be obtained as follow:

  • Half-life (t½) = 1600 years
  • Number of half-lives (n) = 5
  • Time (t) =?

t = n × t½

t = 5 × 1600

t = 8000 years

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