Dual nature of matter was proposed by de Broglie in 1923, it was experimentally verified by Davisson and Germer by diffraction experiment. Wave haracter of matter has significance only for microscopic particles. De Broglie wavelength `(lambda)` can be calculated using the relation, `(lambda) = (h)/(m v)`
where 'm' and 'v' are the mass and velocity of the particle.
Planck's constant has same dimension as that of

Options

A. work
B. energy
C. power
D. angular momentum

Answer

To determine the dimension of Planck's constant, we need to analyze its relationship with other physical quantities. Let's break down the steps:

### Step-by-Step Solution:

1. **Understanding Planck's Constant**:
- Planck's constant (h) is a fundamental constant in quantum mechanics that relates the energy of a photon to the frequency of its associated electromagnetic wave.

2. **Using the Formula**:
- The formula for Planck's constant in terms of energy (E) and frequency (ν) is:
\[ E = hν \]
- Rearranging this gives:
\[ h = \frac{E}{ν} \]

3. **Identifying the Dimensions**:
- The dimension of energy (E) is given in joules (J). In terms of base SI units, 1 joule is:
\[ 1 \text{ J} = 1 \text{ kg} \cdot \text{m}^2/\text{s}^2 \]
- The dimension of frequency (ν) is:
\[ \text{Frequency} = \frac{1}{\text{Time}} = \text{s}^{-1} \]

4. **Substituting Dimensions**:
- Substitute the dimensions of energy and frequency into the equation for Planck's constant:
\[ h = \frac{\text{kg} \cdot \text{m}^2/\text{s}^2}{\text{s}^{-1}} = \text{kg} \cdot \text{m}^2 \cdot \text{s}^{-1} \]

5. **Final Result**:
- Therefore, the dimension of Planck's constant (h) is:
\[ [h] = \text{kg} \cdot \text{m}^2 \cdot \text{s}^{-1} \]
- This shows that Planck's constant has the same dimensions as angular momentum, which is also expressed as mass times velocity times radius.

### Conclusion:
Thus, the Planck's constant has the same dimension as that of angular momentum.