Photoelectric Effect

Step 1: Use de Broglie's wavelength formula. The de Broglie wavelength is given by: Where , , and .
Step 2: Substitute the values:

Step 1: Understanding the photoelectric effect.
According to the photoelectric effect, electrons are ejected from a photo-sensitive material when it absorbs photons with energy greater than or equal to a certain threshold. The energy of a photon is given by , where is Planck's constant and is the frequency of the light.
Step 2: Increasing the frequency.
To overcome the threshold and emit electrons, we need photons with energy greater than the threshold energy. Since energy is proportional to frequency, increasing the frequency will increase the photon energy and thus overcome the threshold.
Step 3: Conclusion.
Hence, the correct answer is option (4).

Final Answer:

Step 1: Use Einstein photoelectric equation.

Step 2: Substitute values.
Given:

Energy of photon:

Step 3: Convert joule to eV.


Step 4: Subtract work function.

Final Answer:

Step 1: Use Einstein’s photoelectric equation.

Step 2: Convert wavelength.

Step 3: Calculate photon energy.


Step 4: Subtract work function.

Step 5: Convert into eV.

Final Answer:

In electric field photoelectron will experience force and accelerate opposite to the field so its increases (ie, stopping potential will increase), no change in photoelectric current, and threshold wavelength.

Step 1: Use stopping potential relation.
Step 2: For .
Given .
Step 3: For .
Step 4: Subtract the equations to remove .
Step 5: Use energy in eV form.
So,
Step 6: Find stopping potential for .
Final Answer:

Step 1: Use Einstein's photoelectric equation.
Step 2: Write given condition.
Initially,
Finally,
Step 3: Compare both equations.
Step 4: Conclude range of .
Since ,
Also to increase energy, must decrease compared to :
Thus,
Final Answer:

Step 1: Use relation for kinetic energy.
Step 2: For frequency .
Step 3: For frequency .
Step 4: Compare with .
Since , denominator is smaller than numerator scale, so ratio becomes greater than 4.
Thus,
Final Answer:

Step 1: Understand arrangement.
Emitter plate is below and collector plate is above.
Electrons move upward from emitter to collector.
Step 2: Direction of applied electric field.
Electric field is vertically downward.
Force on electron is:
So if is downward, electron force is upward.
Step 3: Effect on electrons.
Since force is upward, electrons accelerate more while moving to collector.
Hence their kinetic energy increases.
Step 4: Eliminate other options.
Saturation current does not increase because it depends on number of emitted electrons (intensity).
Stopping potential depends on maximum kinetic energy at emission, not after acceleration.
Threshold wavelength depends on work function, not field.
Final Answer:

Step 1: Use Einstein's photoelectric equation.
The kinetic energy of the emitted electrons is given by: where is Planck’s constant, is the frequency of light, and is the work function of the material.
Step 2: Explanation.
Doubling the frequency of incident light doubles the kinetic energy of the emitted electrons, as is directly proportional to the frequency of the incident light.
Final Answer:

Step 1: Use the photoelectric equation.
The maximum kinetic energy of the emitted electrons is given by: The speed of the emitted electrons is related to the kinetic energy.
Step 2: Calculation of speed ratio.
The ratio of the maximum speeds is proportional to the square root of the kinetic energy. The ratio of the speeds is therefore .
Final Answer:

The stopping potential is related to the kinetic energy of the emitted electrons. The stopping potential can be calculated using the equation , where , and is the electron charge. The stopping potential comes out to be 0.5V.

Step 2: Conclusion.
The correct stopping potential is 0.5V, corresponding to option (b).

The variation in induced emf is due to the variation in the current passing through the coil. The emf will be directly proportional to the current variation over time.

Step 2: Conclusion.
The induced emf varies with time in the same manner as the current, corresponding to option (d).

X-rays are used to create images by passing through dense structures and casting shadows. If the intensities do not provide sufficient contrast, X-rays will pass through them without providing useful diagnostic information.

Step 2: Conclusion.
The correct answer is (c) the X-rays will pass through the intensities without causing a good shadow for any useful diagnosis.

Using the photoelectric effect equation , where is the frequency, we can calculate whether photoelectrons are emitted. Only metal B has sufficient energy to emit photoelectrons.

Step 2: Conclusion.
Photoelectrons are emitted by metal B alone, corresponding to option (b).

Using the photoelectric equation , where is the frequency, is Planck's constant, and is the work function of the metal, we can calculate the cut-off voltage. With the given frequency, the cut-off voltage comes out to be approximately 3V.

Step 2: Conclusion.
The cut-off voltage is 3V, corresponding to option (b).

Threshold energy of is





Similarly,
As the incident photons have energy greater than but less than .
So, photoelectrons will be emitted from metal only

Stopping potential Maximum

Step 1: Using the photoelectric equation.
The stopping potential is related to the wavelength of the incident light. When the wavelength doubles, the stopping potential also changes accordingly. We calculate the threshold wavelength for the given condition.

Step 2: Conclusion.
The threshold wavelength is , corresponding to option (1).

The photoelectric effect occurs when light of sufficient frequency strikes a metallic surface, causing the emission of electrons. Yellow light has a higher frequency than green light, which is why it can cause the ejection of electrons even at the same intensity.

Using the photoelectric equation , where is the kinetic energy, is Planck's constant, is the frequency of light, and is the work function, we can calculate the stopping potential for different wavelengths. For light with a longer wavelength, the stopping potential decreases.

The saturation current in a photocell is inversely proportional to the square of the distance between the light source and the photocell, based on the inverse square law for light intensity.

When electrons strike a metal surface, they can be emitted with a maximum energy equal to the incident energy minus the work function , which is the minimum energy required to release the electron from the metal.

Step 1: Energy of Photoelectron.
The energy of a photoelectron is related to the frequency of the incident light: where is Planck’s constant, is the frequency, and is the work function of the metal.
Step 2: Doubling Wavelength.
Since frequency is inversely proportional to the wavelength, doubling the wavelength results in reducing the frequency by half. Therefore, the energy of the emitted electron will decrease by a factor of 4.
Step 3: Conclusion.
The correct answer is (D), .

Step 1: Understanding the Effect of Wavelength.
According to the photoelectric equation: where is the energy of the photons and is the frequency. Reducing the wavelength increases the frequency and thus increases the energy of the incoming photons.
Step 2: Conclusion.
As energy increases, the cut-off voltage (the minimum stopping potential) required to stop the emitted electrons will increase.
Step 3: Conclusion.
The correct answer is (D), Cut off voltage will increase.

Hologram is based on the phenomenon of interference.

Step 1: The stopping potential is related to the energy of the incoming photons by the equation: where is the frequency of the radiation.
Step 2: For wavelength , the energy of the photons is half of the energy for . Therefore, the stopping potential decreases, and the new stopping potential is:
Final Answer:

The energy of the photon is given by: Substitute , to find the photon energy. Then use the photoelectric equation: Solving gives the work function as 1.51 eV.
Final Answer:

Photon energy: