Question

Calculate the nuclear binding energy per nucleon for 136^Ba if its nuclear mass is 135.905 amu.

Answer 1

1.312 x 10⁻¹² J/nucleon

Step-by-step explanation:

mass of ¹³⁶Ba = 135.905 amu

¹³⁶Ba contain 56 proton and 80 neutron

mass of proton = 1.00728 amu

mass of neutron = 1.00867 amu

mass of ¹³⁶Ba = 56 x 1.00728 amu + 80 x 1.00867 amu

= 137.10128 amu

mass defect = 137.10128 - 135.905

= 1.19628 amu

mass defect = 1.19628 x 1.66 x 10⁻²⁷ Kg

= 1.9858 x 10⁻²⁷ Kg

speed of light = 3 x 10⁸ m/s

binding energy,

E = mass defect x c²

E = 1.9858 x 10⁻²⁷ x (3 x 10⁸)²

E = 17.87 x 10⁻¹¹ J/atom

now,

binding energy per nucleon =
`(17.87* 10^(-11))/(136)`

= 0.1312 x 10⁻¹¹ J/nucleon

= 1.312 x 10⁻¹² J/nucleon