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Chapter 5: Problem 116

The mass of one hydrogen atom is \(1.67 \times 10^{-24}\) gram. Find the mass of 80,000 hydrogen atoms. Express the answer in scientific notation.

Short Answer

Expert verified
The mass of 80,000 hydrogen atoms is \(1.336 \times 10^{-19}\) gram.

Step by step solution

01

Identification of provided values

In the exercise, it's given that the mass of one hydrogen atom is \(1.67 \times 10^{-24}\) gram and we need to find out the mass of 80,000 hydrogen atoms.
02

Multiply the individual mass by the total number of atoms

To find the mass of 80,000 atoms, we multiply the mass of one hydrogen atom by 80,000. So, \(1.67 \times 10^{-24} \times 80,000\). When multiplying with scientific notation, we multiply the coefficients (the numbers) and add the exponents. Here, we are multiplying a number in scientific notation with a whole number, so we only multiply the whole number with the coefficient.
03

Calculating and expressing in scientific notation

After multiplying, we get \(13.36 \times 10^{-20}\) gram. Now, to convert this into correct scientific notation, the coefficient should be between 1 and 10. So shift the decimal one place to the left to get \(1.336 \times 10^{-19}\) gram. The decimal shifted one place to the left, so the exponent increases by 1.

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