To find the difference between the sizes of a hydrogen atom and an oxygen atom, we first need to convert both sizes to scientific notation and make sure they are in similar exponential forms.
The size of a hydrogen atom is given as:
\[ 1.2 \times 10^{-10} , \text{m} \]
The size of an oxygen atom:
\[ 0.000000000152 , \text{m} = 1.52 \times 10^{-10} , \text{m} \]
Now, we can find the difference between the sizes:
\[ \text{Difference} = 1.52 \times 10^{-10} , \text{m} - 1.2 \times 10^{-10} , \text{m} \]
To perform this subtraction, we can align them:
\[ \begin{align*} 1.52 \times 10^{-10} \
- 1.20 \times 10^{-10} \ \hline \end{align*} \]
Now, subtract the coefficients:
\[ 1.52 - 1.20 = 0.32 \]
So the result is:
\[ 0.32 \times 10^{-10} \]
To express this in proper scientific notation, we convert \(0.32\) into scientific notation as \(3.2 \times 10^{-1}\). Therefore:
\[ 0.32 \times 10^{-10} = 3.2 \times 10^{-1} \times 10^{-10} = 3.2 \times 10^{-11} \]
Thus, the difference between the sizes of the hydrogen and oxygen atoms in scientific notation is:
\[ \boxed{3.2 \times 10^{-11}} , \text{m} \]
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