The defining physical characteristic of any colloidal solution is the specific size dimension of its — Surface Chemistry Chemistry Question
Question
The defining physical characteristic of any colloidal solution is the specific size dimension of its dispersed particles. The diameter of valid colloidal particles strictly falls within the narrow range of $1\text{ nm}$ to $1000\text{ nm}$. If the absolute upper limit of this dimensional size range ($1000\text{ nm}$) is expressed mathematically in units of Angstroms ($\text{\AA}$) as $10^z\text{ \AA}$, what is the exact positive integer value of $z$?
💡 Solution & Explanation
The fundamental conversion between nanometers and meters is $1\text{ nm} = 10^{-9}\text{ m}$. The conversion for Angstroms is $1\text{ \AA} = 10^{-10}\text{ m}$. Therefore, $1\text{ nm} = 10\text{ \AA}$. The strict upper limit for colloidal particle size is $1000\text{ nm}$. Converting this entirely to Angstroms: $1000\text{ nm} \times 10\text{ \AA/nm} = 10,000\text{ \AA}$. Expressing $10,000$ exponentially gives exactly $10^4\text{ \AA}$. Therefore, $z = 4$.