Approximately how many electrons are needed to equal the mass of a single proton?

• A. About 18 electrons
• B. About 10,000 electrons
• C. About 1,836 electrons
• D. About 183 electrons

Answer: (C)

Verified step by step guidance

1. Step 1: Understand the problem - We want to find how many electrons have a combined mass equal to the mass of one proton.
2. Step 2: Recall the masses - The mass of a proton is approximately \$1.67 \times 10^{-27}\( kg, and the mass of an electron is approximately \)9.11 \times 10^{-31}$ kg.
3. Step 3: Set up the ratio - To find the number of electrons needed to equal the mass of one proton, divide the proton's mass by the electron's mass: \(\text{Number of electrons} = \frac{m_{\text{proton}}}{m_{\text{electron}}}\).
4. Step 4: Substitute the values into the ratio - \(\text{Number of electrons} = \frac{1.67 \times 10^{-27}}{9.11 \times 10^{-31}}\).
5. Step 5: Interpret the result - The quotient will give the approximate number of electrons needed to have the same mass as one proton, which is close to 1836 electrons.