Minimum de-Broglie wavelength is associated with.

Options

A. Electron
B. Proton
C. `CO_2` molecule
D. `SO_2` molecule

Explanation

To determine which particle has the minimum de-Broglie wavelength, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the de-Broglie Wavelength Formula**:
The de-Broglie wavelength (λ) is given by the formula:
\[ \lambda = \frac{h}{mv} \]
where \( h \) is Planck's constant, \( m \) is the mass of the particle, and \( v \) is its velocity.

2. **Analyze the Relationship**:
From the formula, we can see that the de-Broglie wavelength is inversely proportional to the mass (m) of the particle. This means that as the mass increases, the wavelength decreases.

3. **Identify the Masses of Different Particles**:
- Mass of an electron (m_e) is approximately \( 9.11 \times 10^{-31} \) kg.
- Mass of a proton (m_p) is approximately \( 1.67 \times 10^{-27} \) kg.
- Mass of CO2 (Carbon Dioxide) is \( 12 + 32 = 44 \) g/mol (which is \( 44 \times 10^{-3} \) kg).
- Mass of SO2 (Sulfur Dioxide) is \( 32 + 32 = 64 \) g/mol (which is \( 64 \times 10^{-3} \) kg).

4. **Compare the Masses**:
- Mass of SO2 > Mass of CO2 > Mass of Proton > Mass of Electron
- Therefore, the order from largest to smallest mass is: SO2 > CO2 > Proton > Electron.

5. **Determine the Minimum Wavelength**:
Since the de-Broglie wavelength is inversely proportional to mass, the particle with the largest mass will have the smallest de-Broglie wavelength. In this case, SO2 has the largest mass among the options considered.

6. **Conclusion**:
Thus, the minimum de-Broglie wavelength is associated with the particle that has the largest mass, which is SO2.

### Final Answer:
The minimum de-Broglie wavelength is associated with SO2.

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