According to de Broglie, matter has a wave character. still we cannot measure the wavelength of even 1 mg mass. It is because:

Options

A. actually it does not have a wave character
B. wavelength of particle cannot be measured
C. the diffraction grating required to measure it will be impossibly small
D. it can be measured

Answer

To solve the question, we need to understand the de Broglie hypothesis and how it relates to the wavelength of matter, particularly for a mass of 1 mg.

### Step-by-Step Solution:

1. **Understanding de Broglie's Hypothesis**:
According to de Broglie, all matter exhibits wave-like properties. The wavelength (λ) associated with a particle can be calculated using 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. **Convert Mass to Kilograms**:
The mass given is 1 mg, which we need to convert to kilograms for consistency in SI units:
\[ 1 \text{ mg} = 1 \times 10^{-3} \text{ g} = 1 \times 10^{-6} \text{ kg} \]

3. **Substituting Values into the de Broglie Equation**:
To find the wavelength, we need to substitute the mass into the de Broglie equation. However, we also need to consider a realistic velocity for this mass. For simplicity, let's assume a very small velocity (for example, \( v = 1 \text{ m/s} \)):
\[ \lambda = \frac{h}{mv} = \frac{6.626 \times 10^{-34} \text{ Js}}{(1 \times 10^{-6} \text{ kg})(1 \text{ m/s})} \]

4. **Calculating the Wavelength**:
Plugging in the values:
\[ \lambda = \frac{6.626 \times 10^{-34}}{1 \times 10^{-6}} = 6.626 \times 10^{-28} \text{ m} \]
This wavelength is extremely small, on the order of \( 10^{-28} \) meters.

5. **Conclusion on Measurement**:
The wavelength calculated is so small that it is not feasible to measure it using any conventional methods. The diffraction grating or any measuring device would require a wavelength comparable to the size of the obstacles (like the grating itself) to observe any wave-like behavior. Since the wavelength is far too small, it becomes impossible to measure.

### Final Answer:
We cannot measure the wavelength of even 1 mg mass because the wavelength calculated using de Broglie's equation is extremely small, making it impractical for measurement with conventional methods.