The radius of the hydrogen atom in the ground state is of the order of

Options

A. 1.06 Å
B. 0.265 Å
C. 0.175 Å
D. 0.53 Å

Answer

To determine the radius of the hydrogen atom in the ground state, we can follow these steps:

### Step 1: Understand the Hydrogen Atom
The hydrogen atom consists of one proton in its nucleus and one electron that orbits around the nucleus. The atomic number of hydrogen is 1, which means it has one electron.

**Hint:** Remember that the atomic number indicates the number of protons and electrons in a neutral atom.

### Step 2: Identify the Ground State
The ground state of an atom is its lowest energy state. For hydrogen, the electron occupies the first energy level (n=1).

**Hint:** The ground state corresponds to the electron being in the lowest possible energy level.

### Step 3: Use the Bohr Model
According to the Bohr model of the atom, the radius of the electron's orbit in the ground state can be calculated using the formula:
\[ r_n = n^2 \cdot \frac{h^2}{4 \pi^2 k e^2 m} \]
For hydrogen, this simplifies to:
\[ r_1 = 0.53 \, \text{Å} \]
where:
- \( r_1 \) is the radius of the first orbit,
- \( h \) is Planck's constant,
- \( k \) is Coulomb's constant,
- \( e \) is the charge of the electron,
- \( m \) is the mass of the electron.

**Hint:** The radius for hydrogen in the ground state is a known constant, often memorized as approximately 0.53 Å.

### Step 4: Compare with Given Options
Now that we have determined that the radius of the hydrogen atom in the ground state is approximately 0.53 Å, we can compare this with the provided options:
1. 1.06 Å
2. 0.265 Å
3. 0.175 Å
4. 0.53 Å

**Hint:** Look for the option that matches the calculated value.

### Step 5: Conclusion
From the options provided, the correct answer is 0.53 Å, which is the radius of the hydrogen atom in the ground state.

**Final Answer:** The radius of the hydrogen atom in the ground state is of the order of 0.53 Å.

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