Problem

Calculate the electric potential at the surface of a silver nucleus having a radius of $3.4 \times 10^{-14} \, \mathrm{m}$. The atomic number of silver is $47$, and the charge on a proton is $1.6 \times 10^{-19} \, \mathrm{C}$.

Data

• Radius: $r = 3.4 \times 10^{-14} \, \mathrm{m}$
• Atomic number: $Z = 47$
• Charge on proton: $e = 1.6 \times 10^{-19} \, \mathrm{C}$
• Total charge: $q = Z \cdot e = 47 \cdot 1.6 \times 10^{-19} = 7.52 \times 10^{-18} \, \mathrm{C}$
• Coulomb’s constant: $k = 9 \times 10^9 \, \mathrm{Nm^2C^{-2}}$

Prerequisite Concepts

• Electric Potential at Surface:

$$V = k \frac{q}{r}$$

Answer

Step 1: Apply the Potential Formula

$$V = k \frac{q}{r}$$

Step 2: Substitute Values

$$V = \frac{(9 \times 10^9)(7.52 \times 10^{-18})}{3.4 \times 10^{-14}}$$

Step 3: Simplify

$$V = \frac{67.68 \times 10^{-9}}{3.4 \times 10^{-14}}$$ $$V = 1.99 \times 10^6 \, \mathrm{V}$$

Final Answer

The electric potential at the surface of the silver nucleus is $1.99 \times 10^6 \, \mathrm{V}$.

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