First, let's express both sizes in scientific notation.
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The size of a hydrogen atom is given as \(1.2 \times 10^{-10} \text{ m}\).
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The size of an oxygen atom is \(0.000000000152 \text{ m}\), which can be expressed in scientific notation as follows:
\[ 0.000000000152 = 1.52 \times 10^{-10} \text{ m} \]
Now that we have both sizes in scientific notation:
- Hydrogen atom: \(1.2 \times 10^{-10} \text{ m}\)
- Oxygen atom: \(1.52 \times 10^{-10} \text{ m}\)
To find the difference between the sizes of the hydrogen atom and the oxygen atom, we subtract the size of the hydrogen atom from the size of the oxygen atom:
\[ 1.52 \times 10^{-10} \text{ m} - 1.2 \times 10^{-10} \text{ m} \]
We can do this subtraction directly:
\[ (1.52 - 1.2) \times 10^{-10} \text{ m} = 0.32 \times 10^{-10} \text{ m} \]
Now we express \(0.32\) in scientific notation.
\[ 0.32 = 3.2 \times 10^{-1} \]
Thus, combining this with \(10^{-10}\):
\[ 0.32 \times 10^{-10} \text{ m} = 3.2 \times 10^{-1} \times 10^{-10} \text{ m} = 3.2 \times 10^{-11} \text{ m} \]
So, the difference between the sizes of these atoms, expressed in scientific notation, is:
\[ \boxed{3.2 \times 10^{-11} \text{ m}} \]
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