PLEASE PROVIDE STEP BY STEP, EASY TO FOLLOW AND TO UNDERSTAND, AND HOW YOU APPLI

Question

PLEASE PROVIDE STEP BY STEP, EASY TO FOLLOW AND TO UNDERSTAND, AND HOW YOU APPLIED THE FORMULAR AND THE EXLANATION OF THE FORMULAR IN SOLVING THE FOLLOWING PROBLEM

QUESTION #1

Initially there are 6*10 power 9 radioactive of element "w" (decay constant 0.173/day) in a sample. As a nucleus of "w" decays, it converts 2.67*10 power -28 kg of its mass to energy and releases the energy. How much time ( in days) is required for sample to release a total of 7.2*10 power -4 J?

(A) 0, (B) 0.000290, (C)0.00571, (D) 0.00943, (E) 0.0137, (A,B) 0.0290 , ( A,C) 0.0571, (A,D) 0.290 ,(A,E) 0.571, (B,C) 3.29

Explanation / Answer

Equation: E = mc^2 = (2.67E-28)(3E8)^2 = 2.4E-11 J Number of nuclei that need to decay n = 7.2E-4/(2.4E-11) = 3E7 Decay equation: n[t]=n[0]e^-kt n[t]=n[0]-3E7=6E9-3E7=5.97E9 5.97E9=6.0E9e^-.173t ln(5.97E9/6.oE9)=-.173t t=0.029 days

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