Question

he isotope 81Thallium204 has a half-life of 3.78 years and can be used as a nanotechnology MEMS (Micro Electric Mechanical System) power source device. It decays through beta emission into 82Pb204 with a branching ratio of 97.1 percent with an average decay energy of 0.764 MeV. It also decays through electron capture to 80Hg204 with a branching ratio of 2.9 percent with a decay energy of 0.347 MeV.

Calculate the energy release per decay event in [MeV/disintegration]

Calculate its total specific activity in [Becquerels / gm].

Calculate its total specific activity in [Curies / gm].

Calculate the specific power generation in [Watts(th) / gm].

For a 100 Watts of thermal power in a Radioisotope Heating Unit (RHU) power generator, how many grams of 81Thallium204 are needed?

After 3.78 years of operation, what would its power become?

Use: 1 MeV/sec=1.602x10-13 Watts, Av=0.602x1024 [nuclei/mole], 1 Curie=3.7x1010 Bq.

Answer 1

1. Energy release per decay event = ( 0.9710.764 + 0.029 0.347 ) MeV = 0.752 MeV

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2. Specific activity = dN/dt per 1 gram = N per 1 gram

number of atoms N in 1 gm Thallium = Avagadro number / (Mass of 1 mole of Thallium)

number of atoms N in 1 gm Thallium = ( 6.02 10²³ / 204 ) = 2.951 10²¹

Specific activity = N = [ ln2 / (3.78 365 24 3600) ] 2.951 10²¹

Specific activity = 1.716 10¹³ Bq/g

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3. Specific activity in Curie = [ 1.716 10¹³ Bq/g] / [ 3.7 10¹⁰ ] = 463.76 Ci / g

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4. Specific power generation

Specific power = Specific activity energy released per disintgration

Specific power = 1.716 10¹³ 0.752 MeV

Specific power = 1.716 10¹³ 0.752 1.602 10^-13 = 2.067 W

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5. Required mass of Thallium m_Th for 100 W Thermal power

m_Th = 100 /2.067 = 48.37 g

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6. After 3.78 years , i.e., after one half-life period of Thallium , activity becomes half

Since Power is directly proportional to activity , power will become half of initial power , i.e., 50 W