Question

1.Which type of radioactive emission is analogous to an electron being emitted?

positron, neutrons, alpha particle, gamma rays, beta particle

2. Which isotope is naturally radioactive?

⁴₂H, ²₁H, ¹⁶₈O, ²³⁴₈₈Ra

3. the half life of protactinium-231 is 3.5x10⁴ years. How long will it take for 10.4 grams of Pa-231 to decay to 2.6 grams?

4. the half life of phorphorous-33 is 25.3 days. How long will it take for 64 grams of p-33 to decay to 1.0 grams?

5. the half life of sr-83 is 32.4 hours. how many emissions are produced when 20 g of strontium-83 decas to 4.0 grams?

Answer 1

1. Beta radiation takes the form of either an electron or a positron ,a particle with the size and
mass of an electron, but with a positive charge being emitted from an atom.So,Beta-particle
radiation is analogous to an electron being emitted.

2. ²³⁴Ra₈₈ isotope is naturally radioactive one among the given

3. t_1/2=3.5*10⁴years
  t_1/2= ln2 / λ
  λ=ln2 / 3.5*10⁴ = 1.9804*10^-5
N = N_oe^{- λt} substitute N= 2.6 gms and N_o =10.4gms
   2.6 = 10.4 * e^{-1.9804*10^(-5) *t}
   0.25 =  e^{-1.9804*10^(-5) *t} apply ln on both sides,
ln(0.25) = ln ( e^{-1.9804*10^(-5) *t})
ln(0.25) = -1.9804*10^(-5) * t
t = 70,000.7256 years

4. t_1/2 = 25.3 days
      λ= ln2/25.3 = 0.0273971
solution very much similar to previous problem,
1 = 64 * e^{-0.0273971 *t}
ln(0.015625) = - 0.0273971*t
   t = 151.8 days

5. t_1/2=32.4 hours
     λ=ln2/32.4 = 0.021393
4 = 20 * e^{-0.021393 *t}
t= 75.232 hours
The rate of particle emission be N, N emissons are made during 75.232 hours
The rate of particle emission = λ * number of radioactive nuclei present
N/75.232 = λ * 83
N= 133.5833 =134 emissons are made