Q.4
Q.4 V2V, + V2 V, M and M denote the atomic masses of the parent and the daughter nuclei respectively in a radioactive decay. The Q-value for a ß-decay is QI and that for a decay is Qz. If me denotes the mass of an electron, then which of the following statements is CORRECT ? Q QI Q2 t I me : (A) Q, = & 2me)c2 (C) Q -My - 2me) & (M. -My +2 --—-frhe energy released by the fission of a single uranium nucleus is 200 MeV. The number of fissions of uranium nucleus per second required to produce 16 MW of power is:- (Assume emciency of the reactor is 50%) 200 MeVitTtl 16 50%

Dear student

i n b e t a m i n u s d e c a y M_{X} = M_{Y} + 1 e^{- 1} I n t h i s r e a c t i o n t h e r e i s n o c h a n g e i n m a s s n u m b e r . B u t a t o m i c n u m b e r o f Y i n c r e a s e s b y o n e . L e t t h e a t o m i c n u m b e r o f X i s Z s o a t o m i c n u m b e r o f Y i s (Z + 1) M a s s o f n u c l e u s o f X = (M_{X} - Z m_{e}) M a s s o f n u c l e u s o f Y = (M_{Y} - (Z m_{e} + 1 m_{e})) m a s s o f p r o d u c t = M a s s o f n u c l e u s o f Y + m a s s o f e l e c t r o n = (M_{Y} - (Z m_{e} + 1 m_{e})) + m_{e} = M_{Y} - Z m_{e} M a s s o f n u c l e u s o f X - m a s s o f p r o d u c t = (M_{X} - Z m_{e}) - (M_{Y} - Z m_{e}) = (M_{X} - M_{Y}) s o e n e r g y r e l e a s e d i s = (M_{X} - M_{Y}) c^{2} i n b e t a p l u s d e c a y M_{X} = M_{Y} + 1 e^{+ 1} I n t h i s r e a c t i o n t h e r e i s n o c h a n g e i n m a s s n u m b e r . B u t a t o m i c n u m b e r o f Y d e c r e a s e s b y o n e . L e t t h e a t o m i c n u m b e r o f X i s Z s o a t o m i c n u m b e r o f Y i s (Z - 1) M a s s o f n u c l e u s o f X = (M_{X} - Z m_{e}) M a s s o f n u c l e u s o f Y = (M_{Y} - (Z m_{e} - 1 m_{e})) m a s s o f p r o d u c t = M a s s o f n u c l e u s o f Y + m a s s o f e l e c t r o n = (M_{Y} - (Z m_{e} - 1 m_{e})) + m_{e} = M_{Y} - Z m_{e} + 2 m_{e} M a s s o f n u c l e u s o f X - m a s s o f p r o d u c t = (M_{X} - Z m_{e}) - (M_{Y} - Z m_{e} + 2 m_{e}) = (M_{X} - M_{Y} - 2 m_{e}) s o e n e r g y r e l e a s e d i s = (M_{X} - M_{Y} - 2 m_{e}) c^{2} R e g a r d s

View Full Answer