Question

Calculate the energy (in MeV) released when a decay converts uranium 232u (atomic mass = 232.037146 u) into thorium 228Th (atomic mass = 228.028731 u). The atomic mass of an a particle is 4.002603 u. 9.65MeV Submit Answer Incorrect. Tries 4/10 Previous Tries

Answer 1

Solution : given: mass of uranium 32 is Mo = 232.037146 mass of thorium 228th in M = 228.028731u mass of a particle is M = 4.0026034 loss of mass in dodecay is ..m= mo - (Maht m.) um - [232.037146 - ( 228.028 731 447.002603)]u Am = 0.005812 u { 14 = 1.66X10 27 kg We know that Einstein's mass-energy relation E = mc2/ where (= 3x109 m/s 'c'is speed of light in vacuum so energy released in d-decay is E = ame² = (0.005812x1.6681027, (3x10 27 E = 10.005812* 1.6681027) xq X106 1.641013 Mev E = 5.427 Mev/

Answer 2

SOLUTION :

mass lost in decay 

= m_u - m_t - m particle 

= 232.037146 - 228.02873 - 4.002603 

= 0.005813 amu .

= 0.005813 * (1.6 * 10^(-27) )  kg         (1 amu = 1.6*10^(-27) kg) 

= 9.3008 * 10^(-30) kg 

Now, energy released , E 

= m c^2 

= 9.3008 * 10^(-30) * (3*10^8)^2        (c = speed of light = 3*10^8 m/s)

= 8.37072 * 10^(-13) kg.m/s^2 * m (= N-m = J)

= 8.3702 * 10^(-13) J

= 8.3702 * 10^(-13) / (1.6 * 10^(-19))  ev     ( 1 ev = 1.6*10^(-19) J)

= 5.231375 * 10^6 

= 5.231375 Mev (ANSWER).