To express the mass of 1,000 protons in scientific notation, we can start by expressing the given value \( 1.67 \times 10^{-21} \) grams for a single proton.
Since we want to compute the mass of 1,000 protons, we multiply this value by 1,000:
\[ \text{Mass of 1,000 protons} = 1,000 \times 1.67 \times 10^{-21} \]
Now, converting 1,000 into scientific notation, we have:
\[ 1,000 = 1.0 \times 10^{3} \]
Now we multiply the two expressions:
\[ \text{Mass of 1,000 protons} = 1.0 \times 10^{3} \times 1.67 \times 10^{-21} \]
Multiplying the coefficients:
\[ 1.0 \times 1.67 = 1.67 \]
And adding the exponents:
\[ 10^{3} \times 10^{-21} = 10^{3 - 21} = 10^{-18} \]
Combining these results gives:
\[ \text{Mass of 1,000 protons} = 1.67 \times 10^{-18} \text{ grams} \]
Thus, the mass of 1,000 protons in scientific notation is:
\[ \boxed{1.67 \times 10^{-18} \text{ grams}} \]
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