# Rate of cathodic reaction vs Tafel slope

One of my reference engineering books says that for the cathodic protection process (in seawater):

Al $$\rightarrow$$ Al$$^{3+}$$ + $$3e^-$$ (anode, setting the protection potential at about -900 mV SCE)

2H$$_2$$O + 2$$e^- \ \rightarrow$$ H$$_2$$ + 2OH$$^-$$

Book says that the rate of hydrogen evolution grows roughly one order of magnitude every -120mV of over-polarization (more negative potential). I found online that the Tafel slope for the hydrogen evolution process is roughly $$\beta$$=200 mV/dec in seawater (should be $$\beta$$=120mV for uni-molecular mechanisms). Following this reasoning, I get (using the Tafel equation):

ln$$\frac{i*}{i}$$=ln10=-$$\frac{1}{\beta} \left ( \eta^*-\eta \right )$$

therefore the rate should rise one order of magnitude every $$\Delta\eta$$=460 mV ($$\beta=200mV$$, and $$\Delta\eta$$=276 mV if $$\beta=120 mV$$). Does anybody see any mistake in my reasoning? If this is correct either my Tafel constant is off (should be about 55 mV) or the book has a typo...