Question

Which of the following represents de Broglie equation?

• A. \(\lambda = \frac{h}{\sqrt{mv}}\)
• B. \(\lambda = \frac{h}{mv}\)
• C. \(\lambda = \frac{h}{mp}\)
• D. \(\lambda = \frac{\mu}{p}\)

Hint:

The de Broglie equation \(\lambda = h/p\) is fundamental. Since p=mv, the two forms \(\lambda = h/p\) and \(\lambda = h/mv\) are equivalent and frequently used. Remember that this equation links a particle property (momentum) to a wave property (wavelength).

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
The de Broglie hypothesis relates the wave nature of matter to its particle nature, establishing the dual nature of matter.
Step 2: Key Formula or Approach:
The fundamental de Broglie relationship states that the wavelength ($\lambda$) of a moving particle is inversely proportional to its momentum ($p$). Use the definition of momentum ($p = m \times v$) to find the expanded form.
Step 3: Detailed Explanation:
The de Broglie equation is given by:
\[ \lambda = \frac{h}{p} \]
Where:
$\lambda$ = de Broglie wavelength
$h$ = Planck's constant ($6.626 \times 10^{-34} \text{ J s}$)
$p$ = momentum of the particle
Since momentum ($p$) is the product of mass ($m$) and velocity ($v$), we can substitute $p = mv$:
\[ \lambda = \frac{h}{mv} \]
Step 4: Final Answer:
The correct representation of the de Broglie equation is $\lambda = \frac{h}{mv}$.