If the mass of a proton is `1.67times10^(-24)` gram, what is the number of grams in the mass of 1,000 protons?

Options

A. `1.67times10^(-27)`
B. `1.67times10^(-23)`
C. `1.67times10^(-22)`
D. `1.67times10^(-21)`

Answer

To find the mass of 1,000 protons when the mass of a single proton is given as \(1.67 \times 10^{-24}\) grams, we can follow these steps:

### Step 1: Identify the mass of one proton
The mass of one proton is given as:
\[ \text{Mass of 1 proton} = 1.67 \times 10^{-24} \text{ grams} \]

### Step 2: Calculate the mass of 1,000 protons
To find the mass of 1,000 protons, we multiply the mass of one proton by 1,000:
\[ \text{Mass of 1,000 protons} = 1,000 \times \text{Mass of 1 proton} \]
Substituting the value of the mass of one proton:
\[ \text{Mass of 1,000 protons} = 1,000 \times (1.67 \times 10^{-24}) \]

### Step 3: Simplify the multiplication
We can express 1,000 as \(10^3\):
\[ \text{Mass of 1,000 protons} = 10^3 \times (1.67 \times 10^{-24}) \]

### Step 4: Combine the powers of ten
When multiplying numbers in scientific notation, we add the exponents:
\[ \text{Mass of 1,000 protons} = 1.67 \times (10^3 \times 10^{-24}) = 1.67 \times 10^{3 - 24} = 1.67 \times 10^{-21} \text{ grams} \]

### Final Answer
Thus, the mass of 1,000 protons is:
\[ \text{Mass of 1,000 protons} = 1.67 \times 10^{-21} \text{ grams} \]

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