In a hydrogen atom the electron and proton are at a distance of `0.5 Å`. The dipole moment of the system is .

Answer

To find the dipole moment of a hydrogen atom where the electron and proton are separated by a distance of 0.5 Å, we can follow these steps:

### Step 1: Understand the Concept of Dipole Moment
The dipole moment (P) of a system consisting of two equal and opposite charges is given by the formula:
\[ P = Q \times d \]
where:
- \( Q \) is the magnitude of one of the charges,
- \( d \) is the distance between the charges.

### Step 2: Identify the Charges
In a hydrogen atom:
- The charge of the electron (\( Q_e \)) is \( -1.6 \times 10^{-19} \) coulombs.
- The charge of the proton (\( Q_p \)) is \( +1.6 \times 10^{-19} \) coulombs.

Since we are interested in the magnitude for dipole moment calculation, we can use \( Q = 1.6 \times 10^{-19} \) coulombs.

### Step 3: Convert Distance to Meters
The distance given is \( 0.5 \) Å. We need to convert this to meters:
\[ 1 \text{ Å} = 10^{-10} \text{ m} \]
Thus,
\[ 0.5 \text{ Å} = 0.5 \times 10^{-10} \text{ m} = 5 \times 10^{-11} \text{ m} \]

### Step 4: Calculate the Dipole Moment
Using the formula for dipole moment:
\[ P = Q \times d \]
Substituting the values we have:
\[ P = (1.6 \times 10^{-19} \text{ C}) \times (5 \times 10^{-11} \text{ m}) \]
\[ P = 8 \times 10^{-30} \text{ C m} \]

### Step 5: Final Result
Thus, the dipole moment of the hydrogen atom is:
\[ P = 8 \times 10^{-30} \text{ C m} \]

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