which of the following postulates of the Bohr model led to the quantization of energy of the hydrogen atom ?

Options

A. the electron goes around the nucleus in circular orbits.
B. the angular momentum of the electron can only be an intergral multiple of `h//2pi`.
C. the magnitude of the linear momentum of the electron is qunatized.
D. Quantization of energy is itself a postulate of the bohr model.

Explanation

To determine which postulate of the Bohr model led to the quantization of energy of the hydrogen atom, we can analyze the options provided:

1. **Electron can go around the nucleus in a circular orbit.**
- This statement describes the motion of the electron but does not inherently lead to the quantization of energy. It simply states that electrons orbit the nucleus in a circular path.

2. **Angular momentum of the electron can be an integral multiple of \(\frac{h}{2\pi}\).**
- This is a key postulate of the Bohr model. According to this postulate, the angular momentum \(L\) of the electron in its orbit is quantized and can be expressed as:
\[ L = n \frac{h}{2\pi} \]
where \(n\) is a positive integer (1, 2, 3, ...), and \(h\) is Planck's constant. This quantization of angular momentum directly leads to the quantization of energy levels in the hydrogen atom.

3. **Magnitude of the linear momentum of the electron is quantized.**
- While the linear momentum can be related to the quantization of energy, this statement is not one of the primary postulates of the Bohr model. The quantization of energy levels is primarily derived from the quantization of angular momentum.

Based on the analysis above, the correct answer is:

**The second statement: Angular momentum of the electron can be an integral multiple of \(\frac{h}{2\pi}\).**

### Step-by-Step Solution:

1. **Identify the postulates of the Bohr model.**
- The Bohr model includes several key postulates regarding the behavior of electrons in atoms.

2. **Evaluate the first statement.**
- The first statement describes the electron's orbit but does not lead to quantization of energy.

3. **Evaluate the second statement.**
- The second statement introduces the concept of quantized angular momentum, which is crucial for deriving the quantized energy levels of the hydrogen atom.

4. **Evaluate the third statement.**
- The third statement mentions linear momentum, which is not a primary postulate leading to energy quantization in the Bohr model.

5. **Conclude the analysis.**
- The second statement is the only one that directly leads to the quantization of energy in the hydrogen atom.