Question

The mass of an electron is $9.1\times {10}^{-31}$ kg while the mass of a proton is $1.67\times {10}^{-27}$ kg. Which among the proton and electron has the larger mass?

• A. Proton
• B. Electron
• C. Both have the same mass
• D. Cannot be determined

Answer 1

The correct option is A Proton

Mass of an electron $=9.1\times {10}^{-31}$ kg
Mass of a proton $=1.67\times {10}^{-27}$ kg

$\underset{–}{\text{First Method}}$

Step 1:
Write the numbers in scientific notation. Here, the masses $9.1\times {10}^{-31}$ kg and $1.67\times {10}^{-27}$ kg are already in scientific notation.

Step 2:
Compare the exponents of numbers. The larger the exponent, the greater the number.
$\because -27>-31$
$⟹1.67\times {10}^{-27}>9.1\times {10}^{-31}$

Therefore, proton has a greater mass than the mass of an electron.

$\underset{–}{\text{Second Method}}$

We can compare the masses by making the same exponents to the base $10$.

We would make the powers of $10$ as $-31$ for both the masses.

For proton's mass $1.67\times {10}^{-27}$, to make the exponent of $10$ as $-31,$ we need to multiply ${10}^{-4}$ with ${10}^{-27}$. And, that we can acheive by moving the decimal point in $1.6700$ by $4$ units to the right.

Hence,
Mass of an electron $=9.1\times {10}^{-31}$ kg
Mass of a proton $=16700\times {10}^{-31}$ kg

Now, we can compare the masses of electron and proton by comparing the respective coefficients as both the exponents of $10$ are equal to $-31$.

The number with the larger coefficient is greater.

$\because 16700>9.1$
$⟹16700\times {10}^{-31}>9.1\times {10}^{-31}$, i.e., the mass of proton is greater than the mass of an electron.

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