StudentAidUnit 21: Nuclear Physics — Numericals
12th Class Physics · Unit 21: Nuclear Physics
21.1.Find the mass defect and binding energy of the deuteron nucleus. The experimental mass of deuteron is 3.3435 × 10^{-27} kg.
Formula
Mass defect formula
Δm = (mp + mn) - m2
Working
Substituting proton, neutron, and deuteron masses
Δm = (1.6726 × 10-27 + 1.6749 × 10-27) - 3.3435 × 10-27
Result
Mass defect
Δm = 3.9754 × 10-30 kg
Formula
Binding energy formula
B.E = Δm × c2
Working
Substituting mass defect and speed of light
B.E = (3.9754 × 10-30) × (9 × 1016)
Binding energy in joules
B.E = 3.5729 × 10-13 J
Converting to MeV
B.E = frac{3.5729 × 10-13{1.6 × 10-19 = 2.33 × 106 eV
The book prints 2.33 MeV on this line, but 3.5729 × 10⁻¹³ ÷ 1.6 × 10⁻¹⁹ = 2.233 × 10⁶ eV. Its own Result block gives the correct 2.23 MeV.
Result
Binding energy
B.E = 2.23 MeV
21.2.Iodine –131 is an artificial radioactive isotope. It is used for the treatment of human thyroid gland. Its half life is 8 days. In the drug store of a hospital 20 mg of iodine –131 is present. It was received from the laboratory 48 days ago. Find the quantity of iodine –131 in the hospital after this period.
Given
Initial mass of iodine-131
m0 = 20 mg
Half-life
t1/2 = 8 days
Time elapsed
t = 48 days
Number of half-lives
n = frac{t}{t1/2 = 488 = 6
After 8 days (1 half-life)
m = 20 × 12 = 10 mg
After 16 days (2 half-lives)
m = 20 × left(12right)2 = 5 mg
After 24 days (3 half-lives)
m = 20 × left(12right)3 = 2.5 mg
After 32 days (4 half-lives)
m = 20 × left(12right)4 = 1.25 mg
After 40 days (5 half-lives)
m = 20 × left(12right)5 = 0.625 mg
Result
Quantity after 48 days (6 half-lives)
m = 20 × left(12right)6 = 2064 = 0.3125 mg
21.3.How much energy is absorbed by a man of mass 80 kg who receives a lethal whole body equivalent dose of 400 rem in the form of low energy neutrons for which RBE factor is 10?
Given
RBE factor
RBE = 10
Equivalent dose
De = 400 rem
Mass of man
m = 80 kg
Convert rem to Sv
De = 400 rem = 400 × 0.01 Sv = 4 Sv
Formula
Dose equation
D = frac{De}{RBE
Working
Calculating dose
D = frac{4 Sv{10} = 0.4 Gy
Note on units
1 Gy = 1 J kg-1
Formula
Total energy absorbed
E = m × D
Result
Energy absorbed by the whole body
E = 80 × 0.4 = 32 J