The aim of this study is to demonstrate how the logarithmic millimeter continuum gradient observed using the Atacama Large Millimeter/submillimeter Array (ALMA) may be used to estimate optical thickness in the solar atmosphere. We discuss how using multi-wavelength millimeter measurements can refine plasma analysis through knowledge of the absorption mechanisms. Here we use sub-band observations from the publicly available science verification (SV) data, whilst our methodology will also be applicable to regular ALMA data. The spectral resolving capacity of ALMA SV data is tested using the enhancement coincident with an X-ray Bright Point (XBP) and from a plasmoid ejection event near active region NOAA12470 observed in Band 3 (84-116 GHz) on 17/12/2015. We compute the interferometric brightness temperature light-curve for both features at each of the four constituent sub-bands to find the logarithmic millimetre spectrum. We compared the observed logarithmic spectral gradient with the derived relationship with optical thickness for an isothermal plasma to estimate the structures optical thicknesses. We conclude, within 90% confidence, that the stationary enhancement has an optical thickness between $0.02 leq tau leq 2.78$, and that the moving enhancement has $0.11 leq tau leq 2.78$, thus both lie near to the transition between optically thin and thick plasma at 100 GHz. From these estimates, isothermal plasmas with typical Band 3 background brightness temperatures would be expected to have electron temperatures of $sim 7370 - 15300$ K for the stationary enhancement and between $sim 7440 - 9560$ K for the moving enhancement, thus demonstrating the benefit of sub-band ALMA spectral analysis.
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