Avogadro's number

Also called Avogadro constant, N_0, N_A

Avogadro's number is the count of atoms or molecules in one mole, 6.02 times 10 to the twenty-third per mole. It converts between the two ways the AP gas equations count a sample, moles and individual atoms.

The AP Physics 2 table of information prints it as $N_0$ , not the $N_A$ most textbooks use:

N_0 = 6.02 \times 10^{23}\ \text{mol}^{-1}

Its job on this course is conversion. The sheet prints the ideal gas law twice over, $PV = nRT = Nk_BT$ , and the two halves count the same gas in different currency: $n$ moles, or $N$ atoms. Avogadro's number is the exchange rate.

N = nN_0

It also ties the two gas constants together. Multiply the sheet's own rounded values:

N_0k_B = (6.02 \times 10^{23})(1.38 \times 10^{-23}) = 8.31\ \text{J/(mol} \cdot \text{K)}

which is the printed universal gas constant to three significant figures. Doing that once is worth the minute: it shows the two forms of the gas law are one equation, and it lets you recover either constant if you have misread the other.

Watch the units. $N_0$ carries $\text{mol}^{-1}$ , so $nN_0$ comes out as a pure count. To get the mass of a single atom from a molar mass you divide by $N_0$ , never multiply, and that is the step that feeds $m$ into $v_{\text{rms}} = \sqrt{3k_BT/m}$ after the molar mass has been converted to kilograms per mole.

The value appears on one of the four AP tables of information, the AP Physics 2 one. The AP Physics 1 and both Physics C constants boxes do not list it.

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