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

Options

A. `2pi r = n lambda`
B. `lambda =(h)/( p)`
C. ` pi r^(2) = n lambda`
D. ` 2pi r= ( nh)/ ( lambda)`

Answer

To solve the question "Which of the following equation was suggested by de-Broglie?", we will analyze the options given and identify the correct equation based on de-Broglie's contributions to quantum mechanics.

### Step-by-Step Solution:

1. **Understanding de-Broglie's Contribution**:
- Louis de Broglie proposed the concept of wave-particle duality, suggesting that particles such as electrons exhibit both wave-like and particle-like properties. This is a fundamental idea in quantum mechanics.

2. **Identifying the de-Broglie Equation**:
- The key equation suggested by de Broglie relates the wavelength (λ) of a particle to its momentum (p). The equation is:
\[ \lambda = \frac{h}{p} \]
- Here, \(h\) is Planck's constant, and \(p\) is the momentum of the particle, which can be expressed as \(mv\) (mass times velocity).

3. **Analyzing the Options**:
- Let's look at the options provided:
- **Option A**: \(2 \pi r = n \lambda\) - This relates to the quantization of angular momentum in circular orbits, not de Broglie's equation.
- **Option B**: \(\lambda = \frac{h}{p}\) - This is the correct de Broglie equation.
- **Option C**: \(\pi r^2 = n \lambda\) - This does not relate to de Broglie's work.
- **Option D**: \(2 \pi r = \frac{nh}{\lambda}\) - This is also related to quantization in circular orbits, not de Broglie's equation.

4. **Conclusion**:
- Based on the analysis, the equation suggested by de Broglie is:
\[ \lambda = \frac{h}{p} \]
- Therefore, the correct answer is **Option B**.