An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (2)
Express Avogadro's number, 602 , 200 , 000 , 000 , 000 , 000 , 000 , 000 , in scientific notation.
Move the decimal point 23 places to the left to obtain 6.022 , which is approximately 6.02 .
Multiply 6.02 by 1 0 23 to represent the original number: 6.02 × 1 0 23 .
The correct answer is 6.02 × 1 0 23 .
Explanation
Understanding Scientific Notation We are asked to express Avogadro's number, which is approximately 602 , 200 , 000 , 000 , 000 , 000 , 000 , 000 , in scientific notation. Scientific notation is a way of writing very large or very small numbers in the form a × 1 0 b , where 1 ≤ ∣ a ∣ < 10 and b is an integer.
Converting to Scientific Notation To convert 602 , 200 , 000 , 000 , 000 , 000 , 000 , 000 to scientific notation, we need to move the decimal point to the left until we have a number between 1 and 10. In this case, we move the decimal point 23 places to the left to get 6.022 .
Expressing in Scientific Notation Since we moved the decimal point 23 places to the left, we multiply 6.022 by 1 0 23 to get 6.022 × 1 0 23 . Since the options use 6.02 instead of 6.022 , we can approximate Avogadro's number as 6.02 × 1 0 23 .
Selecting the Correct Option Comparing our result with the given options, we see that option D, 6.02 × 1 0 23 , is the correct answer.
Final Answer Therefore, Avogadro's number in scientific notation is 6.02 × 1 0 23 .
Examples
Avogadro's number is used in chemistry to relate the macroscopic properties of substances (like mass) to the microscopic properties (like the number of atoms or molecules). For example, if you have 12 grams of carbon-12, you have approximately Avogadro's number of carbon atoms. This allows chemists to perform calculations that link the weight of a substance to the number of atoms or molecules present, which is crucial for understanding chemical reactions and material properties. Understanding scientific notation is essential for expressing and manipulating these very large or very small quantities.
Approximately 2.81 × 1 0 21 electrons flow through the device delivering a current of 15.0 A for 30 seconds. This calculation is based on the total charge delivered and the charge of a single electron. The relationship between current, charge, and time is key in determining the number of electrons.
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