Wave Nature Of Matter

The de Broglie wavelength ( ) of a particle is given by the equation: Where: - is Planck's constant ( ), - is the momentum of the particle. Since both the proton and the electron have the same kinetic energy ( ), we can equate their kinetic energies. The kinetic energy is related to momentum as: Where is the mass of the particle and is its momentum. Rearranging this equation to solve for momentum, we get: Now, since the proton and the electron have the same kinetic energy, their momentum will depend on their masses. The mass of the proton ( ) is much greater than the mass of the electron ( ), so the momentum of the proton will be greater than that of the electron. This means that the de Broglie wavelength will be inversely proportional to the momentum.
Thus, for the same kinetic energy, the electron, having a smaller mass, will have a smaller momentum and, therefore, a larger de Broglie wavelength compared to the proton.
In summary, the electron has a greater de Broglie wavelength because it has a smaller mass and therefore smaller momentum for the same kinetic energy.

Step 1: Understanding polarization.
Polarization refers to the orientation of oscillations in the direction perpendicular to the direction of the wave. Light waves, radio waves, and X-rays are transverse waves, meaning their oscillations can be polarized. However, sound waves are longitudinal waves, and they cannot be polarized.
Step 2: Elimination of options.
- (A) Sound waves: Sound waves are longitudinal waves and cannot be polarized.
- (B) Light waves: Light waves are transverse waves and can be polarized.
- (C) Radio waves: Radio waves are also transverse waves and can be polarized.
- (D) X-rays: X-rays are electromagnetic waves and can be polarized.
Conclusion: Sound waves cannot be polarized.