A sample of radium has a weight of 1.5 mg and a half-life of approximately 6 years. How much of the sample will remain after 6 years?
mg

The duration of decay is the same as the half-life of radium, therefore,

half the mass  of radium will remain after 6 years.

Response:

The given mass of the sample of radium, N₀ = 1.5 mg

The half-life of radium = 6 years

Required:

The amount of the sample that will remain after 6 years

Solution:

Let N(t) represent the mass of the sample that remains after 6 years, we have;

Which gives;

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0.75 mg

Step-by-step explanation:

From the question given above the following data were obtained:

Original amount (N₀) = 1.5 mg

Half-life (t₁/₂) = 6 years

Time (t) = 6 years

Amount remaining (N) =.?

Next, we shall determine the number of half-lives that has elapse. This can be obtained as follow:

Half-life (t₁/₂) = 6 years

Time (t) = 6 years

Number of half-lives (n) =?

n = t / t₁/₂

n = 6/6

n = 1

Finally, we shall determine the amount of the sample remaining after 6 years (i.e 1 half-life) as follow:

Original amount (N₀) = 1.5 mg

Half-life (t₁/₂) = 6 years

Number of half-lives (n) = 1

Amount remaining (N) =.?

N = 1/2ⁿ × N₀

N = 1/2¹ × 1.5

N = 1/2 × 1.5

N = 0.5 × 1.5

N = 0.75 mg

Thus, 0.75 mg of the sample is remaining.

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