To determine the number of carbon atoms in a given mass of carbon, we need to use Avogadro's constant and the molar mass of carbon.
Avogadro's constant (Nₐ) is approximately equal to 6.022 x 10²³ particles/mol, and the molar mass of carbon (C) is approximately 12.01 g/mol.
Since 12 grams of carbon is equal to the molar mass of carbon (1 mole), we can calculate the number of carbon atoms in 12 Planck's mass of carbon.
1 Planck's mass is approximately equal to 2.1765 x 10⁻⁸ kg.
First, let's convert the mass of carbon from Planck's mass to grams: Mass of carbon = 12 Planck's mass * (2.1765 x 10⁻⁸ kg/Planck's mass) * (1000 g/kg)
Next, let's calculate the number of moles of carbon: Number of moles = Mass of carbon / Molar mass of carbon
Finally, we can calculate the number of carbon atoms: Number of carbon atoms = Number of moles * Avogadro's constant
Let's perform the calculations:
Mass of carbon = 12 * (2.1765 x 10⁻⁸ kg/Planck's mass) * (1000 g/kg) = 0.26118 g
Number of moles = 0.26118 g / 12.01 g/mol = 0.021737 mol
Number of carbon atoms = 0.021737 mol * 6.022 x 10²³ particles/mol ≈ 1.310 x 10²² carbon atoms
Therefore, there are approximately 1.31 x 10²² carbon atoms in 12 Planck's mass of carbon at NTP (Normal Temperature and Pressure).