Q#1 Initially there are 6*10power9 radioactive ofelement w (decay constant 0.173

Question

Q#1 Initially there are 6*10power9 radioactive ofelement w (decay constant 0.173/day) in a sample. As anucleus of w decays, it converts 2.67 *10power -28 kg of itsmass to energy and releases the energy. How much time(in days) is requirede for the sample to release a total of7.2 *10power -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)0.570 (b,c)3.29 Q#1 Initially there are 6*10power9 radioactive ofelement w (decay constant 0.173/day) in a sample. As anucleus of w decays, it converts 2.67 *10power -28 kg of itsmass to energy and releases the energy. How much time(in days) is requirede for the sample to release a total of7.2 *10power -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)0.570 (b,c)3.29

Explanation / Answer

N = 6*109, = 0.173/day, m = 2.67*10-28kg, E = 7.2*10-4 J, find t initial number of nucleus = N after t, number = Ne-t number reduced = N(1 - e-t) for each nucleus, energy created = mc2 after t, energy generated = mc2N(1 -e-t) = E t = (-1/)ln[1 - E/(mc2N)] = 0.029 days answer: (a,b)

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