To find the difference between the sizes of a hydrogen atom and an oxygen atom, we first convert both given sizes into scientific notation for clarity:
- The size of a hydrogen atom is given as \(1.2 \times 10^{-10} \) m.
- The size of an oxygen atom is given as \(0.000000000152 \) m, which can be converted into scientific notation as \(1.52 \times 10^{-10} \) m.
Next, we'll find the difference between the sizes of the two atoms:
\[ \text{Difference} = \text{Size of Oxygen Atom} - \text{Size of Hydrogen Atom} \] \[ = 1.52 \times 10^{-10} \text{ m} - 1.2 \times 10^{-10} \text{ m} \]
To perform the subtraction, we can align the terms:
\[ 1.52 \times 10^{-10} - 1.2 \times 10^{-10} = (1.52 - 1.2) \times 10^{-10} \] \[ = 0.32 \times 10^{-10} \]
Now, we should express \(0.32\) in scientific notation. To do that:
\[ 0.32 = 3.2 \times 10^{-1} \]
So, now we combine this with the \(10^{-10}\):
\[ 0.32 \times 10^{-10} = 3.2 \times 10^{-1} \times 10^{-10} = 3.2 \times 10^{-11} \]
Thus, the difference between the sizes of the hydrogen atom and the oxygen atom in scientific notation is:
\[ \boxed{3.2 \times 10^{-11} , \text{m}} \]
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