A silver coin with a diameter of 4 cm (such as the U.S. silver dollar) contains 26.96 grams of coin silver and has a surface area of about 27.7 square cm. If the same 26.96 grams of coin silver were divided into particles 1 nanometer in diameter, what would their combined surface area be?
Answers
Explanation:
A silver coin with a diameter of 4 cm (such as the U.S. silver dollar) contains 26.96 grams of coin silver and has a surface area of about 27.7 square cm. If the same 26.96 grams of coin silver were divided into particles 1 nanometer in diameter, what would their combined surface area be?
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Given: The weight of silver in the coin is 26.96 grams and the diameter of the coin is 4 cm.
To find: The combined surface area of the silver particles if 26.96 grams of silver were divided into particles 1 nanometer in diameter.
Solution:
- The surface area of a sphere can be calculated using the formula 4 * π * r^2, where r is the radius of the sphere.
- If the diameter of the silver particle is 1 nanometer, then the radius will be 0.5 nm.
- Substituting this value in the formula, we get:
- 4 * π * 0.5 * 0.5 * 10^-9^2 = 6.283 * 0.25 * 10^-18^ = 1.57 * 10^-18^ cm^2
- Since the total weight of silver in the coin is 26.96 grams, and 1 gram is equal to 10^-6^ kilograms, the total weight of the silver particles will be 26.96 * 10^-6^ kg.
- Since 1 cm^3 of silver weighs 7.87 grams, the volume of the silver particles will be 26.96 * 10^-6^ / 7.87 * 10^-3^ = 3.405 * 10^-14^ cm^3
- The total surface area of the silver particles will be 6 times the surface area of one silver particle, as each particle has six faces.
- Therefore, the total surface area will be 6 * 1.57 * 10^-18^ = 9.42 * 10^-18^ cm^2.
Thus, the combined surface area of the silver particles, if 26.96 grams of silver were divided into particles 1 nanometer in diameter, will be 9.42 * 10^-18^ cm^2.
To learn more about surface area from the given link.
https://brainly.in/question/818113
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