Question

The mass of an electron is approximately equal to $9\times {10}^{-31}$ kg. If the total mass of an atom is $18\times {10}^{-25}$ kg, find the ratio of the mass of an electron to the total mass of an atom.

• A. $\frac{1}{2\times {10}^6}$
• B. $2\times {10}^6$
• C. $\frac{1}{2\times {10}^5}$
• D. $2\times {10}^5$

Answer 1

The correct option is A $\frac{1}{2\times {10}^6}$

$\bullet$ Mass of an electron $=9\times {10}^{-31}$ kg
$\bullet$ Total mass of an atom $=18\times {10}^{-25}$ kg
$\therefore$ Ratio of the mass of an electron to the total mass of an atom $=\frac{\text{Mass of an electron}}{\text{Total mass of an atom}}$

$=\frac{9\times {10}^{-31}}{18\times {10}^{-25}}$

$=\frac{9\times {10}^{-31}}{9\times 2\times {10}^{-25}}$

$=\frac{1}{2\times {10}^{-25}\times {10}^{31}}$ $(\because a^{-n}=\frac{1}{a^n})$


$=\frac{1}{2\times {10}^{-25+31}}$ $(\because a^m\times a^n=a^{m+n})$

$=\frac{1}{2\times {10}^6}$

Therefore, option (a.) is the correct one.