मान लीजिये की रेडियम की अर्ध-आयु 1500 साल है। इसका अर्थ है कि रेडियम अपनी आधी मात्रा का विघटन करने के लिए 1500 साल लेगा, यदि नमूने में 100 ग्राम है, तो इसे 50 ग्राम बनने के लिए कितने वर्ष लगेंगे?

  1. 100 वर्ष
  2. 75 वर्ष
  3. 1500 वर्ष
  4. 125 वर्ष

Answer (Detailed Solution Below)

Option 3 : 1500 वर्ष
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Detailed Solution

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यदि समय t वर्ष में मौजूद रेडियम की मात्रा x(t) है।

सूत्र के अनुसार,

अतः x = x0 ekt

यदि x0 = 100 है, तो x = 100 ekt

दोनों तरफ लघुगुणक करने पर हम पाते हैं कि,

साथ ही,

जब x = 50 है,

t = लगभग 1500 वर्ष

अतः 100 ग्राम रेडियम के 50 ग्राम का विघटन होने के लिए लगभग 1500 वर्ष लगेंगे।

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