Fig. 10

Theoretical relative uncertainties (2σ) of ²⁰⁷Pb/²⁰⁶Pb ratios in Pb with atomic abundances of ²⁰⁶Pb = 25% and ²⁰⁷Pb = 15.5% (corresponding to ²⁰⁷Pb/²⁰⁶Pb = 0.62, a radiogenic isotope composition for a 4555 Ma material) for total amount of Pb from 1 pg to 100 ng. The black lines “zero noise 100% yield” and “zero noise 4% yield” show uncertainties of static multicollector measurements based on counting statistics only, calculated using Eqs. 6–8 and assuming total ion yields of 100% and 4%, respectively. Black dashed line shows uncertainties of peak jumping measurements on a single ion counting multiplier (ion yield 4%, measurement duty cycle 10%, zero amplifier noise). The three colored dashed lines show uncertainties calculated using Eq. 9 and assuming amplifier noise of 4 × 10⁻¹⁶ A/s (equal to Johnson–Nyquist noise for amplifiers with 10¹¹ Ohm resistors) and various times of baseline measurement (base) and signal integration (int) in minutes. The noise-related uncertainty components are calculated using Eqs. 10–11. For all calculations, it is assumed that the ion beam intensity remained constant during analysis, and that signal integration occupied 80% of the total measurement time (duty cycle 80%). The baseline is assumed to be measured outside the useful emission time (e.g., during warmup). The horizontal orange line shows the significance threshold adopted in this study