Questions: Problem 2: (14% of Assignment Value) A 2.5 g copper penny is given a charge of -2.1 nC. - Part (a) ✔️ Which statement best describes the numbers of protons and electrons in the penny when it is charged as indicated? Electrons were added, and the number of electrons exceeds the number of protons. ✔️ Correct: - Part (b) ✔️ How many electrons were transferred in order to create the charge on the penny? Ne=1311 x 10^10 Ne=1.311 x 10^10 electrons ✔️ Correct! Part (c) By what percentage do the transferred electrons change the mass of the penny? (Express your result as a positive percentage for an increase, negative for a decrease.) (Δm/m)= %

Problem 2: (14% of Assignment Value) A 2.5 g copper penny is given a charge of -2.1 nC. - Part (a) ✔️ Which statement best describes the numbers of protons and electrons in the penny when it is charged as indicated? Electrons were added, and the number of electrons exceeds the number of protons. ✔️ Correct: - Part (b) ✔️ How many electrons were transferred in order to create the charge on the penny? Ne=1311 x 10^10 Ne=1.311 x 10^10 electrons ✔️ Correct! Part (c) By what percentage do the transferred electrons change the mass of the penny? (Express your result as a positive percentage for an increase, negative for a decrease.) (Δm/m)= %
Transcript text: Probiem 2: (14\% of Assignment Value) A 2.5 g copper penny is given a charge of -2.1 nC . - Part (a) $\checkmark$ Which statement best describes the numbers of protons and electrons in the penny when it is charged as indicated? Electrons were added, and the number of electrons exceeds the number of protons. $\checkmark$ Correct: - Part (b) $\checkmark$ How many electrons were transferred in order to create the charge on the penny? \[ \begin{array}{l} N_{e}=1311 \times 10^{10} \\ N_{e}=1.311 \times 10^{10} \text { electrons } \end{array} \] $\checkmark$ Correct! Part (c) By what percentage do the transferred electrons change the mass of the penny? (Express your result as a positive percentage for an increase, negative for a decrease.) \[ \frac{\Delta m}{m}=\square \% \] Grade Summary Deductions Potential $0 \%$ Late Work \% $00 \%$
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Solution

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Solution Steps

Step 1: Calculate the Mass of Transferred Electrons

First, we need to calculate the mass of the electrons that were transferred. The mass of a single electron is approximately \(9.109 \times 10^{-31} \, \text{kg}\).

The number of electrons transferred is given as \(N_e = 1.311 \times 10^{10}\).

The total mass of the transferred electrons is: \[ m_e = N_e \times \text{mass of one electron} = 1.311 \times 10^{10} \times 9.109 \times 10^{-31} \, \text{kg} \]

Step 2: Calculate the Mass of the Penny

The mass of the penny is given as 2.5 g, which is equivalent to \(2.5 \times 10^{-3} \, \text{kg}\).

Step 3: Calculate the Percentage Change in Mass

The percentage change in mass due to the transferred electrons is calculated using the formula: \[ \frac{\Delta m}{m} = \left(\frac{m_e}{m_{\text{penny}}}\right) \times 100\% \]

Substitute the values: \[ \frac{\Delta m}{m} = \left(\frac{1.311 \times 10^{10} \times 9.109 \times 10^{-31}}{2.5 \times 10^{-3}}\right) \times 100\% \]

Final Answer

After performing the calculations, the percentage change in the mass of the penny is:

\[ \boxed{\frac{\Delta m}{m} = 4.777 \times 10^{-18} \%} \]

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