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Step 1:I'll solve this problem step by step, following the specified LaTeX formatting guidelines:
Step 2:: Recall the known values of Boltzmann's constant
k_{B} = 1.380649 \times 10^{-23} \mathrm{J/K}
We know its value is:
Step 3:: Convert joules to electron volts
1 \mathrm{eV} = 1.602176634 \times 10^{-19} \mathrm{J}
To convert joules to electron volts, we need to know the conversion factor:
Step 4:: Perform the conversion calculation
k_{B} \text{ in eV/K} = \frac{1.380649 \times 10^{-23} \mathrm{J/K}}{1.602176634 \times 10^{-19} \mathrm{J/eV}}
Step 5:: Calculate the final value
k_{B} = 8.617333262 \times 10^{-5} \mathrm{eV/K}
Final Answer
Boltzmann's constant is 8.617 \times 10^{- 5} \mathrm{eV/K}.
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