The Bohr model of atoms

Options

A. assumes that the angular momentum of electrons is quantized .
B. uses Einstein's photoelectirc equation.
C. predicts continous emission spectra for atoms.
D. predicts the same emission spectra for all types of atoms.

Explanation

### Step-by-Step Solution for the Bohr Model of Atoms

1. **Understanding the Bohr Model**:
The Bohr model was proposed by Niels Bohr in 1913 to explain the behavior of electrons in atoms, particularly hydrogen and hydrogen-like atoms. It describes how electrons orbit the nucleus in specific paths or "orbits".

**Hint**: Remember that the Bohr model is specifically designed for hydrogen and hydrogen-like atoms.

2. **Quantization of Angular Momentum**:
According to the Bohr model, the angular momentum of an electron in orbit is quantized. This means that the angular momentum (L) can only take on certain discrete values, which 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.

**Hint**: Focus on the formula for angular momentum and the significance of \( n \) being an integer.

3. **Quantization of Energy Levels**:
The energy of the electron in these quantized orbits is also discrete. The energy levels can be calculated using the formula:
\[ E_n = -\frac{13.6 \, \text{eV}}{n^2} \]
where \( E_n \) is the energy of the electron in the nth orbit.

**Hint**: Recall that energy levels become less negative (higher) as \( n \) increases.

4. **Emission Spectrum**:
When an electron transitions between these energy levels, it emits or absorbs a photon with energy equal to the difference between the two levels. This results in the emission spectrum of the atom, which consists of discrete lines rather than a continuous spectrum.

**Hint**: Think about how energy transitions lead to spectral lines.

5. **Evaluating Options**:
Given the options in the question:
- Assume that the angular momentum of the electron is quantized (correct).
- Uses Einstein's photoelectric equation (not correct).
- Predict continuous emission spectra for atoms (not correct).
- Predict the same emission spectrum for all types of atoms (not correct).

The correct option is the first one, which aligns with the fundamental principle of the Bohr model.

**Hint**: Cross-check each option against the principles of the Bohr model to determine correctness.

### Summary of the Solution:
The Bohr model applies specifically to hydrogen and hydrogen-like atoms, where the angular momentum and energy levels of electrons are quantized. The only correct statement regarding the Bohr model is that it assumes the angular momentum of the electron is quantized.