Math Problem Statement

An amoeba has 1.5E+06 protons and a net charge of -2.6 pC. Calculate the total number of electrons on the amoeba.

Solution

To calculate the total number of electrons on the amoeba, we need to use the relationship between charge and the number of electrons.

The charge of a single electron is: e=1.6×1019Ce = 1.6 \times 10^{-19} \, \text{C}

Step 1: Determine the net charge

The amoeba has a net charge of 2.6pC-2.6 \, \text{pC}, which is equivalent to: 2.6pC=2.6×1012C-2.6 \, \text{pC} = -2.6 \times 10^{-12} \, \text{C}

Step 2: Calculate the number of electrons

Since the amoeba has a negative charge, this indicates an excess of electrons. The number of electrons (NeN_e) can be calculated by dividing the total charge by the charge of a single electron: Ne=QeN_e = \frac{Q}{e} where:

  • Q=2.6×1012CQ = -2.6 \times 10^{-12} \, \text{C} (net charge of the amoeba)
  • e=1.6×1019Ce = 1.6 \times 10^{-19} \, \text{C} (charge of a single electron)

Ne=2.6×10121.6×10191.625×107electronsN_e = \frac{-2.6 \times 10^{-12}}{1.6 \times 10^{-19}} \approx -1.625 \times 10^7 \, \text{electrons}

Thus, the amoeba has approximately 1.625×1071.625 \times 10^7 excess electrons.

Step 3: Verify with the protons

The amoeba has 1.5×1061.5 \times 10^6 protons. Each proton carries a positive charge equal to the charge of an electron, but the total number of protons does not directly affect the calculation of the net charge due to the excess of electrons.

Final Answer:

The total number of excess electrons on the amoeba is approximately 1.625×1071.625 \times 10^7.

Would you like more details or have any further questions on this? Here are some related questions:

  1. How would the result change if the amoeba had a different net charge?
  2. How do protons and electrons contribute to the overall charge of an object?
  3. What is the role of Coulomb's law in understanding electric charge and forces?
  4. How can we calculate the total charge on a body using the number of protons and electrons?
  5. How do we convert between charge units (like pC, nC, etc.)?

Tip: When working with charges, remember that the charge of a proton is equal in magnitude but opposite in sign to that of an electron.

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Math Problem Analysis

Mathematical Concepts

Charge and Electric Forces
Electron Charge
Protons and Electrons

Formulas

N_e = Q / e
e = 1.6 x 10^-19 C

Theorems

Coulomb's Law

Suitable Grade Level

Grades 9-11