Published by:
CGP EDU Academic Team
Published on: September 12, 2026
The wavelength of the matter wave is independent of
Text Solution
Verified by ExpertsThe correct answer is:
D
Step 1: Understand the de Broglie wavelength. The wavelength of a matter wave, given by the de Broglie relation, is defined as:
$$ \lambda = \frac{h}{p} $$
where
- $\lambda$ is the wavelength,
- $h$ is Planck's constant,
- $p$ is the momentum of the particle.
Step 2: Analyzing the parameters:
- From the equation, we see that the wavelength ($\lambda$) is inversely proportional to the momentum ($p$). This means that if mass or velocity changes, the momentum will change, affecting the wavelength.
- Mass affects the momentum, as $p = mv$.
- Velocity directly influences momentum, meaning changes in velocity lead to changes in the wavelength.
- However, charge does not appear in the de Broglie relation at all.
Conclusion: Therefore, the wavelength of the matter wave is independent of charge. Hence, the correct answer is D.
$$ \lambda = \frac{h}{p} $$
where
- $\lambda$ is the wavelength,
- $h$ is Planck's constant,
- $p$ is the momentum of the particle.
Step 2: Analyzing the parameters:
- From the equation, we see that the wavelength ($\lambda$) is inversely proportional to the momentum ($p$). This means that if mass or velocity changes, the momentum will change, affecting the wavelength.
- Mass affects the momentum, as $p = mv$.
- Velocity directly influences momentum, meaning changes in velocity lead to changes in the wavelength.
- However, charge does not appear in the de Broglie relation at all.
Conclusion: Therefore, the wavelength of the matter wave is independent of charge. Hence, the correct answer is D.
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