The mass of a proton is 1.67 x 10⁻²⁷kg. How many protons would make 1 g ?

The correct option is 5.99x10²³.

To find the number of protons that make up a total mass of 1 g, we need to divide the total target mass by the mass of a single proton. First, let us ensure both masses are expressed in the same unit.

The mass of a single proton is given as:
Mass of one proton = 1.67 × 10^-27 kg

We want to find the number of protons in 1 g. Let us convert the total mass from grams to kilograms:
Total mass = 1 g = 10^-3 kg

Now, let $N$ be the number of protons. The formula to find $N$ is:

$N=\frac{\text{Total mass}}{\text{Mass of one proton}}$

Substituting the values into the equation:

$N=\frac{{10}^{-3}\text{kg}}{1.67\times {10}^{-27}\text{kg}}$

Simplifying the fraction by dividing the numbers and handling the exponents:

$N=\frac{1}{1.67}\times {10}^{-3-(-27)}$

$N\approx 0.5988\times {10}^{24}$

To write this in standard scientific notation, we shift the decimal point one place to the right and adjust the exponent:

$N\approx 5.99\times {10}^{23}$

Therefore, approximately 5.99 × 10²³ protons are required to make 1 g.