Which of the following equation was suggested by de-Broglie?

Options

A. `2pir=nlamda`
B. `lamda=pi/h`
C. `pir^2=nlamda`
D. `2pir=(nh)/lamda`

Answer

To determine which equation was suggested by de Broglie, we need to focus on his contributions to the understanding of wave-particle duality, particularly in relation to matter, such as electrons.

### Step-by-Step Solution:

1. **Understanding de Broglie's Hypothesis**:
- Louis de Broglie proposed that particles, such as electrons, exhibit both wave-like and particle-like properties. This concept is known as wave-particle duality.

2. **De Broglie Wavelength Equation**:
- The de Broglie wavelength (\( \lambda \)) is given by the equation:
\[ \lambda = \frac{h}{mv} \]
- Here, \( h \) is Planck's constant, \( m \) is the mass of the particle, and \( v \) is its velocity. This equation describes how the wavelength of a particle is inversely proportional to its momentum (\( p = mv \)).

3. **Identifying the Correct Equation**:
- Among the options provided (A, B, C, D), we need to identify which one corresponds to the de Broglie wavelength equation.
- The correct equation that represents de Broglie's suggestion is:
\[ \lambda = \frac{h}{p} \]
- This can also be expressed as \( p = mv \), leading to the same conclusion.

4. **Conclusion**:
- The equation suggested by de Broglie is the one that relates the wavelength of a particle to its momentum, which is \( \lambda = \frac{h}{mv} \).