Vardaan Institute - Physics Worksheet (Level 1)

Topic 11.1: Photoelectric Effect & Einstein’s Equation

The work function of Caesium is $2.14 \text{ eV}$. Find the threshold frequency for Caesium. ($h = 6.63 \times 10^{-34} \text{ Js}$)

The threshold frequency for a certain metal is $3.3 \times 10^{14} \text{ Hz}$. If light of frequency $8.2 \times 10^{14} \text{ Hz}$ is incident on the metal, predict the cutoff voltage for the photoelectric emission.

Explain why the wave theory of light could not explain the existence of a threshold frequency in the photoelectric effect.

Light of wavelength $488 \text{ nm}$ is produced by an Argon laser which is used in the photoelectric effect. When light from this spectral line is incident on the emitter, the stopping potential of photoelectrons is $0.38 \text{ V}$. Find the work function of the material from which the emitter is made.

AI Image Prompt: A clean, high-quality, mathematically correct landscape graph showing the variation of stopping potential (V0) on the y-axis with the frequency of incident radiation (nu) on the x-axis for two different metals A and B (Metal A having a lower threshold frequency than B). The graph must show two parallel straight lines with a positive slope, intersecting the x-axis at nu0A and nu0B. The background of the whole image should be fully white.

Filename: Level1_Q5_Stopping_Potential_vs_Frequency.png

From the graph, what physical quantity is represented by the slope of these lines?

Calculate the energy of a photon of frequency $6 \times 10^{14} \text{ Hz}$ in electron volts (eV).

How does the stopping potential of a photoelectric cell change if the distance between the light source and the cell is doubled? Justify your answer.

If the intensity of incident light of a given frequency is increased, how does it affect (i) the maximum kinetic energy of photoelectrons, and (ii) the photoelectric current?

The work function of a metal is $4.2 \text{ eV}$. Will this metal give photoelectric emission for incident radiation of wavelength $330 \text{ nm}$?

10.

Monochromatic light of frequency $6.0 \times 10^{14} \text{ Hz}$ is produced by a laser. The power emitted is $2.0 \times 10^{-3} \text{ W}$. Estimate the number of photons emitted per second on average by the source.

11.

State the three salient features of the photoelectric effect that can only be explained by the photon picture of light.

12.

Define 'Stopping Potential'. Does it depend on the intensity of incident light for a given frequency?

13.

Find the maximum speed of photoelectrons emitted when radiation of frequency $10^{15} \text{ Hz}$ falls on a metal of work function $2.5 \text{ eV}$. ($m_e = 9.1 \times 10^{-31} \text{ kg}$)

14.

A student performs an experiment on photoelectric effect and observes that for a certain frequency of light, no current flows until the collector potential is made positive. Explain this observation using the concept of work function.

15.

What is the significance of the intercept made by the stopping potential vs. frequency graph on the frequency axis?

Topic 11.2: Matter Waves (de Broglie Hypothesis)

16.

Calculate the de Broglie wavelength of an electron moving with a kinetic energy of $100 \text{ eV}$.

17.

An electron, an alpha particle, and a proton have the same kinetic energy. Which of these particles has the shortest de Broglie wavelength?

18.

A particle is moving three times as fast as an electron. The ratio of the de Broglie wavelength of the particle to that of the electron is $1.813 \times 10^{-4}$. Identify the particle using its mass.

19.

What is the de Broglie wavelength associated with an electron, accelerated through a potential difference of $100 \text{ V}$?

20.

AI Image Prompt: A clean, high-quality, mathematically correct landscape graph showing the variation of de Broglie wavelength (lambda) with the magnitude of momentum (p). The graph must show a rectangular hyperbola (lambda inversely proportional to p) in the first quadrant. Label the axes clearly. The background of the whole image should be fully white.

Filename: Level1_Q20_Lambda_vs_Momentum_Graph.png

21.

Calculate the de Broglie wavelength of a ball of mass $0.15 \text{ kg}$ moving with a speed of $30 \text{ m/s}$. Why do we not observe the wave nature of such a ball?

22.

Show that the de Broglie wavelength of a particle of mass $m$ and kinetic energy $K$ is given by $\lambda = \frac{h}{\sqrt{2mK}}$.

23.

Two particles A and B have the same de Broglie wavelength. If particle A has a higher mass than B, which one has the higher kinetic energy?

24.

At what value of accelerating voltage will the de Broglie wavelength of an electron be exactly $1 \text{ \AA}$?

25.

What is the de Broglie wavelength of a neutron in thermal equilibrium with matter at $27^\circ\text{C}$? ($k_B = 1.38 \times 10^{-23} \text{ J/K}$, mass of neutron $= 1.67 \times 10^{-27} \text{ kg}$)

26.

Distinguish between a photon and a material particle like an electron in terms of their rest mass and velocity.

27.

An electron and a proton are accelerated through the same potential difference. Find the ratio of their de Broglie wavelengths.

28.

If the momentum of a particle is doubled, how does its de Broglie wavelength change?

29.

Matter waves are neither electromagnetic nor acoustic. Explain this statement briefly based on the conditions for their existence.

30.

A photon and an electron have the same wavelength. Which one has the higher energy? Justify mathematically.

Topic 11.3: Davisson-Germer Experiment

31.

State the main objective of the Davisson-Germer experiment. What was the major conclusion drawn from it?

32.

In the Davisson-Germer experiment, why was a single crystal of Nickel used instead of a polycrystalline sample?

33.

At what specific values of accelerating voltage and scattering angle was the maximum intensity of scattered electrons observed?

34.

The glancing angle $\theta$ for the Nickel crystal corresponds to a scattering angle $\phi = 50^\circ$. Calculate $\theta$.

35.

AI Image Prompt: A clean, high-quality, mathematically correct landscape polar plot showing electron scattering intensity versus scattering angle (phi) for four different voltages: 40V, 44V, 48V, and 54V. The 54V plot should show a very distinct, large 'bump' at 50 degrees, while the others show smaller or no bumps. The background of the whole image should be fully white.

Filename: Level1_Q35_Davisson_Germer_Voltage_Comparison.png

36.

For a scattering angle of $50^\circ$, the interplanar spacing for Nickel is $d = 0.91 \text{ \AA}$. Using Bragg's law ($n=1$), calculate the wavelength of the electron beam and compare it with the de Broglie wavelength for $54 \text{ V}$.

37.

Why is the Davisson-Germer experiment considered the experimental verification of de Broglie’s hypothesis?

38.

What happens to the intensity of the scattered electron beam as the accelerating voltage is increased from $44 \text{ V}$ towards $54 \text{ V}$ at a fixed angle of $50^\circ$?

39.

Explain the role of the "Electron Gun" and the "Faraday Cylinder" in the Davisson-Germer setup.

40.

If the experiment were repeated with protons instead of electrons, would the peak intensity occur at the same voltage? Why or why not?

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