Half-lives of Daughter Nuclides of Uranium
Emily Wang with Kelley Rivoire
MIT Department of Physics Outline
1. History of Radioactivity
2. Motivations for Experiment
3. Theory: unstable nuclei, nuclide chains
4. Experimental Setup and Procedure
5. Results
6. Conclusions History
• 1896: Becquerel’s photographic plates.
• 1898: Marie Curie’s studies of thorium, discovery of radium.
• 1899: Rutherford names “alpha rays” and “beta rays”.
• 1900: Rutherford, Soddy discover transmutation of elements.
• 1902: Exponential law of radioactive decay. Motivations
• Observe the decay of different isotopes of radon.
• Measure half-lives of Po218 and Pb211 by observing the de- creasing alpha decay activity. The Stability of Nuclei
• Most natural elements with atomic number Z = 1 to Z = 82 are stable. Isotopes of elements with Z > 82 will decay.
• Light nuclei w/ equal numbers of protons, neutrons are sta- ble. Heavier nuclei need more neutrons to overcome Coulom- bic repulsion of protons.
• Three kinds of radioactive transmutation:
– Alpha decay: emission of charged He nucleus (2 neutrons, 2 protons) – Beta decay: emission of (e+ + ν) or (e− +ν ¯). – Spontaneous fission: split into two nuclei. The Bateman Equations
• Determine half-life of isotope B, which decays from A.
dA (−t/τA) • Law of radioactive decay: dt = −A/τA,A(t) = A0e • Solve for B(t) using variation of parameters:
dB – dt = A/τA − B/τB,B(t) = Bh(t) + Bp(t) (−t/τ ) τB (−t/τ ) (−t/τ ) – B(t) = B0e B + A0 [e A − e B ] τA−τB
• Special cases of Bateman Eqs.
τB (−t/τ ) – B(t) ≈ A0 [1 − e B ] when τ τ and t τ τA A B B (−t/τ ) – B(t) ≈ (A0 + B0)e B when τA τB and t τA Experimental Setup +44VDC Detector Bias Supply
Preamplifier Amplifier Oscilloscope Silicon barrier detector Multichannel Uraninite rocks Analyzer
Po+ Po+ HV Source The Silicon Barrier Detector
n-p Junction (with Bias Voltage) Bias Voltage Electrons Holes
• Semi-conductor p-n junctions used.
• Creation of “depletion zone” where there are no charge carriers— length of this zone critical. Decay of Radon Isotopes Thorium Series Uraninum Series Actinium Series Th-232 U-234 U-235
Rn-220 Rn-222 Rn-219 55.6s 3.82d 3.96s Po-216 Po-218 Po-215 0.145s ?? 1.78ms Pb-212 Po-214 Pb-211 10.6h 163us ?? Bi-212 Bi-214 Bi-211 1.01h 19.9min 2.14min Po-212 Tl-207 0.298us 4.77min Sample MCA Calibration Data
4 x 10 Aged Uranite Energy Spectrum (5/5/05) 4.5 Po−218 4 6.00 Po−214 7.69
3.5
3
2.5
Counts 2
1.5 Bi−211 6.62
1 Po−216 Bi−212 6.78 6.05 Po−212 0.5 8.78 MeV
0 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 Calibrated Energy (MeV) Evolution of Energy Spectrum Uranite Energy Spectrum (5/3/05)
12000
10000
8000 6000 Po−214 Counts 4000 Bi−211 2000
0 5.5 6 6.5 7 7.5 8 8.5 9 9.5 Calibrated Energy (MeV)
4 x 10 Uranite Energy Spectrum (5/5/05)
4
3 Po−214 increases 2 Bi−211 Counts Bi−212 Po−212 emerges increases emerges 1
0 5.5 6 6.5 7 7.5 8 8.5 9 9.5 Calibrated Energy (MeV) Exponential Fit to Po218 Decay 300 Bi211 data fit line χ2 = 1.3 250 ν−1
200 λ Fit model: y = Ae−t/
Average value from two runs: 150 τ = 3.13 ± 0.03 min 1/2
Net Counts per Second 100
50
100 200 300 400 500 600 700 Time Elapsed (sec) Exponential Fit to Bi211 Decay 3.5 Bi211 data fit line 3
χ2 = 1.4 2.5 ν−1
λ Fit model: y = Ae−t/ 2
τ = 37.4 ± 0.5 min 1/2 1.5
1 Net Counts per Second
0.5
1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 Time Elapsed (sec) Error Analysis
• Systematic Error: Equipment?
• Random Error: Poisson error in counts, constant error from uncertainty in ROI determinations. Results
• Half life of Po218
– Expt: 3.13 ± 0.03 min
– Accepted: 3.10 min
• Half life of Pb211
– Expt: 37.4 ± 0.5 min
– Accepted: 36.1 min Conclusions
• Observed decay chains of various isotopes of Rn.
• Achieved reasonable agreement with accepted values for half- lives of Pb211 and Po218.