Dual Nature Of Matter

To solve this problem, we start with the de Broglie wavelength formula for an electron:

where is the de Broglie wavelength, is Planck's constant, and is the momentum.

Given that the change in wavelength is , denote the initial momentum as and the final momentum after change as .

The initial wavelength is:

The final wavelength is:

According to the problem, the change in wavelength is of the initial wavelength:

Substituting for and , we have:

Simplifying, we get:

Cross-multiplying gives:

Expanding and simplifying the equation:

Rearranging the terms:

Solving for :

Considering round-off effects and practical implementation, the closest option is:

100 P

In the photoelectric effect, when a photon of energy strikes a photosensitive metallic surface with a work function , electrons can be emitted. The energy of the incoming photon is used to overcome the work function of the metal; any excess energy is converted into the kinetic energy of the emitted electron.

The energy conservation equation for this process can be written as:

where represents the maximum kinetic energy of the emitted electrons.

By rearranging the equation, we find:

This shows that the maximum kinetic energy of the emitted electrons is equal to the energy of the photon minus the work function of the material.

Therefore, the correct statement from the options provided is: Maximum K.E.=h\nu−h\nu_0​.

The photoelectric effect occurs when light incident on a metal surface causes the emission of electrons. The photoelectric current (the rate of electron flow) depends on the intensity of the incident light, which decreases with distance from the light source according to the inverse square law. As the distance from the point source increases, the intensity of the light, and consequently the photoelectric current, decreases proportionally to the square of the distance.

Mathematically, this relationship can be expressed as:

where is the intensity of light, and is the distance from the light source. Therefore, the photoelectric current is also proportional to the reciprocal of the square of the distance.

The correct graph representing this relationship is a curve that shows the photoelectric current decreasing with increasing distance, consistent with the graph labeled as "Graph (II)".

The photoelectric effect can be described using the equation: , where is the kinetic energy of the photoelectrons, is the energy of the incident photons, and is the work function of the metal. Initially, we have the kinetic energy: . When the energy of incident radiation increases by 25%, the new energy becomes .
Correspondingly, the kinetic energy increases to .

Using the equation for the photoelectric effect in both scenarios, we have:

1. For the initial condition:
2. For the increased energy:

By solving these equations simultaneously, we can find the work function . Subtract equation 1 from equation 2:

Which simplifies to:

Solving for :

Substitute back into equation 1:

Solve for :

Thus, the work function of the metal is 0.6 eV.

In Young’s double-slit experiment, the intensity at a point on the screen is given by the formula ,

where is the phase difference between the interfering waves.
The phase difference is related to the path difference by .
Given that at , when .
Now, we need to find when .

Let's calculate:

This implies , giving or .

Hence or .

From , we find or .

The smallest non-zero path difference is .

Therefore, the path difference at a point where the intensity is is .