Conservation Of Energy

The de Broglie wavelength is given by , where is Planck's constant and is the momentum of the particle.
Since momentum is related to the kinetic energy by (where is the mass of the particle), a decrease in leads to a decrease in .
Assuming kinetic energy is decreased by 36%, then . Therefore, .
Since , the new wavelength , which corresponds to a 25% increase.

To determine the mean kinetic energy per molecule of a polyatomic gas with degrees of freedom, we need to use the principle of equipartition of energy. According to this principle, each degree of freedom contributes to the kinetic energy, where is the Boltzmann constant and is the absolute temperature.

For a molecule with degrees of freedom, the total mean kinetic energy per molecule is given by multiplying the contribution per degree of freedom by the number of degrees of freedom:

This result does not depend on the number of Avogadro's number directly, because it pertains to individual molecules rather than a mole of molecules. Therefore, the mean kinetic energy per molecule is:

Thus, the correct answer is the option:

We are given three equal electric charges of charge , placed at the vertices of an equilateral triangle with side length . The task is to find the potential energy of this system.

Step 1: The potential energy of a system of charges is given by the formula:

where , and are the magnitudes of the charges, and is the distance between the charges.

Step 2: For this system, all three charges are of equal magnitude and the distance between any two charges is . Therefore, the potential energy of the system is the sum of the potential energies due to each pair of charges:

Substituting , we get:

Thus, the potential energy of the system is .