Question

The mass of a proton is 1.673 × 10-24 g. The mass of a neutron is 1.675 × 10-24 g. The mass of the nucleus of an 56Fe atom is 9.289 × 10-23 g. What is the nuclear binding energy (in J) for 56Fe? (c = 3.00 × 108 m/s)

Answer 1

Answer:

1.31 X 10^ -10 joules per Fe 56 atom

Explanation:

The mass of a proton is 1.673 × 10-24 g. The mass of a neutron is 1.675 × 10-24 g. The mass of the nucleus of an 56Fe atom is 9.289 × 10-23 g. What is the nuclear binding energy (in J) for 56Fe? (c = 3.00 × 108 m/s)

some of the theoretical mass will be converted to binding energy

by Einstein's famous relativity equation

E = mc^2

where E is in joules, m is in Kgm. c is in m/sec

56Fe is element 26 so it has 26 protons and  56 -26 =30 neutrons

its theoretical nuclear mass is

(26 X 1.673 X 10^-24) + (30X1.675 X 10^-24)  =

(43.498 X 10^-24) + (50.250 X 10^-24)=

93.748 X 10^24 gm

but its actual mass is 9.289 X 10^-23 g or

92.289 X 10^-24 g

the mas defect is the theoretical mass minus the actual

1.459 X 10^-24 gm =^

1.459 X 10^-27 Kgm

c = 3.00 X 10* m/s=

so joules of binding energy = (1.459 X 10^-27) X 9 X10^16)

1.31 X 10^ -10 joules per Fe 56 atom