Home
Class 12
PHYSICS
Assertion: The de-broglie wavelength equ...

Assertion: The de-broglie wavelength equation has significance for any microscopic or submicroscopic particles.
Reason : The de-broglie wavelength is inversely proportional to the mass of the object if velocity is constant.

Text Solution

AI Generated Solution

The correct Answer is:
To solve the given question, we need to analyze both the assertion and the reason provided. ### Step-by-Step Solution: 1. **Understanding the Assertion**: - The assertion states that the de Broglie wavelength equation has significance for any microscopic or submicroscopic particles. - The de Broglie wavelength (\( \lambda \)) is given by the formula: \[ \lambda = \frac{h}{p} \] where \( h \) is Planck's constant and \( p \) is the momentum of the particle. 2. **Understanding the Reason**: - The reason states that the de Broglie wavelength is inversely proportional to the mass of the object if the velocity is constant. - Since momentum \( p \) is defined as \( p = mv \) (where \( m \) is mass and \( v \) is velocity), we can rewrite the de Broglie wavelength as: \[ \lambda = \frac{h}{mv} \] - If the velocity \( v \) is constant, then the de Broglie wavelength \( \lambda \) becomes inversely proportional to the mass \( m \): \[ \lambda \propto \frac{1}{m} \] 3. **Analyzing the Significance**: - For microscopic and submicroscopic particles (like electrons, protons, etc.), the mass is small, which means that the de Broglie wavelength can be significant and measurable. - In contrast, for macroscopic particles (like a baseball or a car), the mass is large, leading to a very small de Broglie wavelength, which is negligible and not significant in practical terms. 4. **Conclusion**: - Both the assertion and the reason are true: - The assertion is true because the de Broglie wavelength is indeed significant for microscopic and submicroscopic particles. - The reason is also true as it correctly explains that the de Broglie wavelength is inversely proportional to mass when velocity is constant. 5. **Final Statement**: - Therefore, both the assertion and reason are true, and the reason is a correct explanation of the assertion. ### Final Answer: - **Assertion**: True - **Reason**: True - **Explanation**: The reason correctly explains the assertion.
Promotional Banner

Similar Questions

Explore conceptually related problems

De Broglie wavelength lambda is proportional to

The de Broglie wavelength is given by

de-Broglie wavelength applies only to

For particles having same K.E., the de-Broglie wavelength is

The de - Broglie wavelength associated with the particle of mass m moving with velocity v is

The de Broglie wavelength associated with particle is

The de-Broglie wavelength of an electron in the first Bohr orbit is

If the kinetic energy of a moving particle is E , then the de-Broglie wavelength is

The de Broglie wavelength of an electron in the 3rd Bohr orbit is

The momentum of a particle associated with de-Broglie's wavelength of 6 Å is