Two radioactive elements X and Y have half-lives of 25 minutes and 75 minutes respectively. Sample of X and Y initially contain equal number of atoms. After 150 minutes, what is the value of the following fraction?No. of nuclei of X unchanged/No. of nuclei of Y unchanged
Correct answer: A. 1: 16
- A. 1: 16
- B. 16: 1
- C. 1: 8
- D. 8: 1
Explanation
Number of half-lives = 150 min / 25 min = 6 half-livesSimilarly, for element Y, with a half-life of 75 minutes, after 150 minutes, we can calculate the number of half-lives as follows:Number of half-lives = 150 min / 75 min = 2 half-livesFor element X: (1/2) ^ 6 = 1/64 For element Y: (1/2) ^ 2 = 1/4Therefore, the fraction of the number of nuclei of X remains unchanged to the number of nuclei of Y remains unchanged is:(1/64) / (1/4) = 1/64 * 4/1 = 1/16 This can be simplified to: 1:16So, the correct answer is option (a) 1:16.
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