Question

Unknown nuclear reaction proceeds by the hypothetical X --> Y + Z. At some beginning time, the activity of a sample is 1.9x10¹⁵ per second and produces 298Watts of power. After one year, the activity of the sample is 1.2x10¹⁵ per second. 1) If it is known that the mass of (Y+Z) is 123.456789012u, what is the mass of X (in u)? 2) What is the expected power output after 4 years from the beginning time?

Answer 1

1)
amount of energy released per per one reaction,

E = 298/(1.9*10^15)

= 1.5684210526*10^-13 J

The amount of mass converted to energy, m = E/c^2

= 1.5684210526*10^-13/(3*10^8)^2

= 1.7426900584*10^-30 kg

= 1.7426900584*10^-30/(1.66054*10^-27)

= 0.00104947189 u

so mass of X = mass of (X + Y) + m

= 123.456789012 + 0.00104947189

= 123.457838483 u <<<<<<<<<<-----------------------Answer

2) Expected power after 4 year, P_new = P_old*(1.2*10^15/(1.9*10^15))

= 298*1.2/1.9

= 188 W <<<<<<<<<<-----------------------Answer