HW Chemical Dose Student name:

CHEMICAL DOSE:

1. Calculate the dose rate and the absorbed dose for the Fricke dosimetric solution that was irradiated with Co-60 source during 3 hrs. The absorbance of the irradiated dosimetric solution (Fe3+), measured with UV/Vis-spectrophotometer in 1 cm cuvettes at the wavelength (=304 nm, increased from 0.01 (initial) to 0.203 (irradiated). The molar absorptivity of ferric ions for this wavelength is ε304 = 2187 L mol‑1cm‑1, the density of the dosimetric solution is ρ=1.024 g/mL, and the tabulated radiation chemical yield for gamma source 60Co is 1.6 µmol J‑1.

2. Calculate the dose rate and the absorbed dose for the ceric sulfate dosimetric solution that was irradiated with Co-60 source during 3 hrs. The absorbance of the irradiated dosimetric solution (Ce4+), measured with UV/Vis-spectrophotometer in 1 cm cuvettes at the wavelength (=320 nm, decreased from 1.01 (initial) to 0.21 (irradiated). The molar absorptivity of ceric ions for this wavelength is ε320 = 561 L mol‑1cm‑1, density of the dosimetric solution is ρ=1.025 g/mL and the G value for the cerous-ion yield is 2.3 molecules/100 eV for the gamma source 60Co.

3. Estimate the effect of alpha-autoradiolysis in the acidic aqueous solution of 239Pu with concentration of 0.03 mol/L of 239Pu:

a) Considering the half-life T1/2=24111 y (=7.60364×1011 sec) and the alpha energy of 5.24 MeV, what is the weekly dose absorbed in 1L solution? E(alpha/Pu) = 5.24 MeV x 1.602.10-19 J/eV = 8.395×10-13 J

b) The plutonium is originally in its hexavalent state, but is reduced to its tetravalent state (then precipitated) by the reaction with hydrogen radicals. If the radiation yield of hydrogen radicals is 0.2 umol/J, how much Pu(VI) is reduced in one week? Hint: [Pu6+ + 2H* = Pu4+ +2H+]

4. The count rates listed in the table below were measured for a mixture of two genetically independent radionuclides. Both radionuclides are beta- emitters, and they both precipitate in the solution of AgNO3. Identify the unknown radionuclides in the measured mixture, and calculate their initial activity (DE = 40%). Recall that precipitating of both the unknown radionuclides with silver nitrate indicates that both unknown elements are halogens.

HINT:

The concentrations of colored solution are usually determined spectrophotometrically. Method is based on the Lambert-Beer law, which binds the absorbance A (decrease of the light beam intensity) with the molar concentration of the analyte C, its molar absorptivity ε (constant at given wavelength) and the length of the light path (thickness of the cuvette with measured liquid):

A = ε.c.l

1. Use the ladder operator formalism for harmonic oscillator to derive the selection rule on

⟨𝑣 ′|(𝑅 − 𝑅𝑒 ) 𝑛 |𝑣”⟩ for arbitrary n.

2. For a heteronuclear diatomic molecule AB, the dipole moment function in the neighborhood of

R=Re is given by

𝜇(𝑅) = 𝑎 + 𝑏(𝑅 − 𝑅𝑒 ) + 𝑐(𝑅 − 𝑅𝑒 ) 2 + 𝑑(𝑅 − 𝑅𝑒 )

3

In which a, b, c and d are constants. Treating this molecule as a harmonic oscillator (using ladder

operator), expand dipole moment in Taylor series around R2 and then calculate the relative intensity

of v=0->1, v=0->2 and v=0->3 transitions in terms of these constant and harmonic oscillator

constants μ and ω.

3. (McHale chapter10. Problem7) A general harmonic potential function for water is

𝑉 = 1

2 𝑘𝑟 (∆𝑟1)

2 + 1

2 𝑘𝑟 (∆𝑟2)

2 + 1

2 𝑘𝜃 (𝑟∆𝜃)

2 + 𝑘𝑟𝑟 ∆𝑟1∆𝑟2 + 𝑘𝑟𝜃 𝑟∆𝑟1∆𝜃 + 𝑘𝑟𝜃 𝑟∆𝑟2∆𝜃

The last three terms contain off-diagonal force constants, while the first three are diagonal. In

matrix form, this can be expressed as 2V=RTFR, where R=(∆𝑟1 ∆𝑟2 ∆𝜃) is the vector whose

elements are the internal coordinates. Find the symmetry coordinates S1, S2 and S3 for water,

and the diagonal force constant f which permits the potential energy in form written STfS

4. For raman spectroscopy, show that the following equation leads to a symmetric tensor, 𝛼𝜌𝜎 =

𝛼𝜎𝜌, in the limit 𝜔0 ≪ 𝜔𝑒𝑔 .

(𝛼𝜌𝜎 )𝑖𝑓 = 1

ℏ ∑[

⟨𝑖|𝜇𝜌|𝑛⟩⟨𝑛|𝜇𝜎 |𝑓⟩

𝜔0 + 𝜔𝑛𝑓 + 𝑖Γ𝑛 −

⟨𝑖|𝜇𝜎 |𝑛⟩⟨𝑛|𝜇𝜌|𝑓⟩

𝜔0 − 𝜔𝑛𝑖 − 𝑖Γ𝑛 ]

𝑛