A radioactive element gets spilled over the floor of a room. Its half-life period is 30 days . If the initial activity is ten times the permissible va - Chemistry MCQ AIEEE 2007 2026 | ExamTest.live

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A radioactive element gets spilled over the floor of a room. Its half-life period is 30 days . If the initial activity is ten times the permissible value, after how many days will it be safe to enter the room?

Solution & Step-by-step Explanation

Let initial activity be A_{0} and permissible activity be A .Given A_{0} = 10 A, so \frac{A _{0}}{A} = 10 .We use the formula: A = A_{0} (1/2)^{n}, where n is the number of half-lives. 1/10 = (1/2)^{n} ⟹ 10 = 2^{n} Taking log on both sides: lo g_{10} 10 = n lo g_{10} 2 1 = n \times 0.3010 ⟹ n = \frac{1}{0.3010} \approx 3.32 Total time t = n \times t_{1/2} : t = 3.32 \times 30 = 99.6 days \approx 100 days

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A radioactive element gets spilled over the floor of a room. Its half-life period is 30 days . If the initial activity is ten times the permissible value, after how many days will it be safe to enter the room?

1000 days

300 days

10 days

100 days

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