To find the difference in sizes between a hydrogen atom and an oxygen atom, we first need to express both sizes in scientific notation.
The size of a hydrogen atom is given as \( 1.2 \times 10^{-10} \) meters.
The size of an oxygen atom is given as \( 0.000000000152 \) m, which can also be expressed in scientific notation as:
\[ 0.000000000152 = 1.52 \times 10^{-10} , \text{m} \]
Now, to find the difference between the sizes of the oxygen and hydrogen atoms:
\[ \text{Difference} = \text{Size of Oxygen} - \text{Size of Hydrogen} \]
Substituting the values we have:
\[ \text{Difference} = 1.52 \times 10^{-10} , \text{m} - 1.2 \times 10^{-10} , \text{m} \]
Subtracting the coefficients gives:
\[ 1.52 - 1.2 = 0.32 \]
Now, we can express \( 0.32 \) in scientific notation:
\[ 0.32 = 3.2 \times 10^{-1} \]
However, we need to adjust for the exponent since the sizes we are dealing with are very small.
The final step is to put \( 0.32 \times 10^{-10} \):
\[ 0.32 \times 10^{-10} = 3.2 \times 10^{-11} \]
Thus, the difference in sizes between the hydrogen and the oxygen atom is:
\[ \boxed{3.2 \times 10^{-11} , \text{m}} \]
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