Please explain the answers thoroughly as well as allthe necessary steps arriving

Question

Please explain the answers thoroughly as well as allthe necessary steps arriving at the answers. Thanks! Some vertebrate bones dug up from an archeological site inMontana were found to be 1.13 x 104 years old. Whatwas the disintegration rate of the bones during“dating” (based on Carbon 14)? Express thisactivity in disintegrations per minute per gram. Assume thehalf life of C 14 to be 5,730 years and the original activity of15.3 disintegrations per minute per gram. Please explain the answers thoroughly as well as allthe necessary steps arriving at the answers. Thanks! Some vertebrate bones dug up from an archeological site inMontana were found to be 1.13 x 104 years old. Whatwas the disintegration rate of the bones during“dating” (based on Carbon 14)? Express thisactivity in disintegrations per minute per gram. Assume thehalf life of C 14 to be 5,730 years and the original activity of15.3 disintegrations per minute per gram.

Explanation / Answer

where A o = initial activity = 15.3disintegrations per minute per gram. A = ? Also we know that decay constant , =0.693 / T T = half life = 5730 years                  = 5730 * 365 * 24 * 60 min So , = 2.3010 * 10^-10 min ^-1 Given time , t = 1.13 x 104years                     = 1.13 x 104 * 365 * 24 * 60 min                     = 593928 * 10^4 min Plug the values in Eq(1) we have  A= Ao e - t                                                       = 3.9 disintegrations per minute per gram.                                                       = 3.9 disintegrations per minute per gram.

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