Question

High-mass radionuclides, which may be either alpha or beta emitters, belong to one of four decay chains, depending on whether their mass number A is of the form 4n, 4n+1, 4n+2, or 4n+3, where n is a positive integer. (a) Justify this statement and show that if a nuclide belongs to one of these families, all its decay products belong to the same family. Classify the following nuclides as to family: (b) ${\mathbf{}}^{\mathbf{235}}\mathbf{U}$(c) localid="1661601960557" ${\mathbf{}}^{\mathbf{236}}\mathbf{U}\mathbf{}$(d) ${\mathbf{}}^{\mathbf{238}}\mathbf{U}$ (e) localid="1661601429038" ${\mathbf{}}^{\mathbf{239}}\mathbf{PU}$ (f) localid="1661601438307" ${\mathbf{}}^{\mathbf{240}}\mathbf{PU}$(g) localid="1661601952668" ${\mathbf{}}^{\mathbf{245}}\mathbf{PU}$ (h) localid="1661601482780" ${\mathbf{}}^{\mathbf{246}}\mathbf{Cm}$ (i) ${\mathbf{}}^{\mathbf{249}}\mathbf{Cf}$and (j) ${\mathbf{}}^{\mathbf{249}}\mathbf{Fm}$.

Short answer

(a) The mass number of nuclides after the decay of alpha and beta particles belongs to the family of mass numbers 4n,4n+1, 4n+2, and 4n+3.

(b) The U-235 belongs to the 4n+3 family of mass numbers.

(c) The U-236 belongs to the 4n family of mass numbers.

(d) The U-238 belongs to the 4n+2 family of mass numbers.

(e) The Pu-239 belongs to the 4n+3 family of mass numbers.

(f) The Pu-240 belongs to the 4n family of mass numbers.

(g) The Cm-245 belongs to the 4n+1 family of mass numbers.

(h) The Cm-246 belongs to the 4n+2 family of mass numbers.

(i) The Cf-249 belongs to the 4n+1 family of mass numbers.

(j) The Fm-253 belongs to the 4n+1 family of mass numbers.

Step-by-step solution

Radioactive decay

Radioactive decay is the process of decaying protons from the nucleus and variation in the mass number of the atom. The number of protons increases by one unit due to beta decay and no change in the mass number of the atom, while the number of protons changes by two units and mass number by four units for alpha decay.

Justification for statement and proof for nuclide belonging to one family of decay(a)

The mass number of nuclides changes by four units in the alpha decay so the mass number of a new nuclide is always of type A - 4n .

Here, A is the mass number of original nuclides and is the number of decayed alpha particles.

The mass number does not change due to the decay of beta particles so the mass number remains unchanged.

The mass number of nuclides for alpha or beta particle decay remains as 4n, 4n+1, 4n+2, and 4n+3.

Therefore, the mass number of nuclides after the decay of alpha and beta particles belongs to the family of mass numbers 4n, 4n+1, 4n+2, and 4n+3.

Classification of the family for nuclide(b)

The mass number of U-235 can be expressed as:

If we compare the above-expressed mass number with 4n+3 for n=58 then U-235 belongs to the 4n+3 family of mass numbers.

Therefore, the U-235 belongs to the 4n+3 family of mass numbers.

Classification of the family for nuclide(c)

The mass number of U-236 can be expressed as:

A = 236

A = 4(59)

If we compare the above-expressed mass number with 4n for n=59 then U-236 belongs to the 4n family of mass numbers.

Therefore, the U-236 belongs to the 4n family of mass numbers.

Classification of the family for nuclide(d)

The mass number of U-238 can be expressed as:

A = 238

A = 4 (59) + 2

If we compare the above-expressed mass number with 4n+2 for n=59 then U-238 belongs to the 4n+2 family of mass numbers.

Therefore, the U-238 belongs to the 4n+2 family of mass numbers.

Classification of the family for nuclide(e)

The mass number of Pu-239 can be expressed as:

A = 239

A = 4(59) + 3

If we compare the above-expressed mass number with 4n+3 for n=59 then Pu-239 belongs to the 4n+3 family of mass numbers.

Therefore, the Pu-239 belongs to the 4n+3 family of mass numbers.

Classification of the family for nuclide(f)

The mass number of Pu-240 can be expressed as:

A = 240

A = 4(60)

If we compare the above-expressed mass number with 4n for n=60 then Pu-240 belongs to the 4n family of mass numbers.

Therefore, the Pu-240 belongs to the 4n family of mass numbers.

Classification of the family for nuclide(g)

The mass number of Cm-245 can be expressed as:

A = 245

A = 4(61) + 1

If we compare the above-expressed mass number with 4n+1 for n=61 then Cm-245 belongs to the 4n+1 family of mass numbers.

Therefore, the Cm-245 belongs to the 4n+1 family of mass numbers.

Classification of the family for nuclide(h)

The mass number of Cm-246 can be expressed as:

A = 246

A = 4(61) + 2

If we compare the above-expressed mass number with 4n+2 for n=61 then Cm-246 belongs to the 4n+2 family of mass numbers.

Therefore, the Cm-246 belongs to the 4n+2 family of mass numbers.

Classification of the family for nuclide(i)

The mass number of Cf-249 can be expressed as:

A = 249

A = 4(62) + 1

If we compare the above-expressed mass number with 4n+1 for n=62 then Cf-249 belongs to the 4n+1 family of mass numbers.

Therefore, the Cf-249 belongs to the 4n+1 family of mass numbers.

Classification of the family for nuclide(j)

The mass number of Fm-253 can be expressed as:

A = 253

A = 4(63) + 1

If we compare the above-expressed mass number with 4n+1 for n=63 then Fm-253 belongs to the 4n+1 family of mass numbers.

Therefore, the Fm-253 belongs to the 4n+1 family of mass numbers.