Question

The half-life of radon gas is approximately four days. Four weeks after the introduction of radon into a sealed room, the fraction of the original amount remaining is closest to

Answer 1

The fraction of the original amount remaining is closest to 1/128

Determination of the number of half-lives

• Half-life (t½) = 4 days
• Time (t) = 4 weeks = 4 × 7 = 28 days
• Number of half-lives (n) =?

n = t / t½

n = 28 / 4

n = 7

How to determine the amount remaining

• Original amount (N₀) = 100 g
• Number of half-lives (n) = 7
• Amount remaining (N)=?

N = N₀ / 2ⁿ

N = 100 / 2⁷

N = 0.78125 g

How to determine the fraction remaining

• Original amount (N₀) = 100 g
• Amount remaining (N)= 0.78125 g

• Fraction remaining =?

Fraction remaining = N / N₀

Fraction remaining = 0.78125 / 100

Fraction remaining = 1/128

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