The dual nature of electron was given by somerfeld

Answer

**Step-by-Step Solution:**

1. **Identify the Claim**: The statement claims that "The dual nature of electron was given by Sommerfeld."

2. **Evaluate the Claim**: To determine if the statement is true or false, we need to recall who actually proposed the dual nature of the electron.

3. **Correct Attribution**: The dual nature of the electron, which refers to the concept that electrons exhibit both particle-like and wave-like properties, was proposed by Louis de Broglie, not Sommerfeld.

4. **Mathematical Expression**: De Broglie introduced a mathematical expression to describe the wavelength (λ) of a particle, which is given by the formula:
\[ \lambda = \frac{h}{p} \]
where:
- \( \lambda \) = wavelength
- \( h \) = Planck's constant
- \( p \) = momentum of the particle

5. **Momentum Relation**: Momentum (p) can also be expressed in terms of mass (m) and velocity (v):
\[ p = mv \]
Therefore, we can rewrite the wavelength formula as:
\[ \lambda = \frac{h}{mv} \]

6. **Conclusion**: Since the original statement attributed the dual nature of the electron to Sommerfeld, and it is actually attributed to de Broglie, the statement is false.

7. **Final Statement**: The correct attribution is that "The dual nature of the electron was proposed by Louis de Broglie."

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