Vardaan Institute - Physics Worksheet (Level 0)

Topic 11.1: Photoelectric Effect & Einstein's Equation

(MCQ) The phenomenon of emission of electrons from a metal surface when light of suitable frequency falls on it is called:

(a) Thermionic emission

(b) Photoelectric effect

(d) Field emission

(MCQ) The minimum energy required by an electron to just escape from the metal surface is known as:

(a) Kinetic energy

(b) Work function

(d) Potential energy

(MCQ) A widely used practical unit of energy in atomic physics, equivalent to $1.6 \times 10^{-19} \text{ J}$, is the:

(a) Erg

(b) Electron volt (eV)

(d) Calorie

(Fill in the blank) The minimum frequency of incident light below which no photoelectric emission takes place is called ____________ frequency.

(Fill in the blank) The number of photoelectrons emitted per second is directly proportional to the ____________ of incident light.

(True/False) The maximum kinetic energy of emitted photoelectrons depends strictly on the intensity of the incident light.

(True/False) Photoelectric emission is an instantaneous process with almost no time lag.

(One Word) What is the discrete quantum packet or bundle of light energy called?

(Formula) Write the formula for the energy ($E$) of a single photon in terms of frequency ($\nu$) and Planck's constant ($h$).

10.

(Formula) State Einstein's photoelectric equation relating incident energy ($h\nu$), work function ($\Phi_0$), and maximum kinetic energy ($K_{max}$).

11.

(MCQ) The negative potential applied to the anode with respect to the cathode that reduces the photoelectric current exactly to zero is called:

(a) Accelerating potential

(b) Stopping potential

(d) Critical potential

12.

(MCQ) If $V_0$ is the stopping potential, then the maximum kinetic energy $K_{max}$ of the photoelectrons is given by:

(a) $e / V_0$

(b) $e V_0$

(d) $e + V_0$

13.

AI Image Prompt: A clean, high-quality, mathematically correct landscape graph showing the variation of Photoelectric Current (y-axis) with Anode Potential (x-axis) for two different INTENSITIES of incident light (I1 and I2, where I2 > I1) but at the SAME FREQUENCY. The graph must show a common negative Stopping Potential (-V0) on the x-axis, branching out into two parallel saturation current levels. The background of the whole image should be fully white.

Filename: Level0_Q13_Photoelectric_Current_vs_Potential.png

14.

(Fill in the blank) The value of Planck’s constant ($h$) is approximately $6.626 \times 10^{-34}$ ____________ (write the SI unit).

15.

(Fill in the blank) Increasing the frequency of incident light (above threshold) will linearly increase the magnitude of the ____________ potential.

16.

(True/False) If the incident frequency is strictly below the threshold frequency, no photoelectrons are emitted, no matter how intense the light is.

17.

(True/False) Light behaves solely as a wave during the photoelectric effect interaction.

18.

(Match the following A to D with 1 to 4)

A. $\nu_0$	1. Work function
B. $\Phi_0$	2. Stopping potential
C. $V_0$	3. Threshold frequency
D. $K_{max}$	4. Maximum kinetic energy

19.

(One Word) Which metal family (e.g., Alkali, Transition, Noble) is most highly sensitive to the photoelectric effect due to their low work functions?

20.

(Formula) Write the formula relating work function ($\Phi_0$) and threshold wavelength ($\lambda_0$).

Topic 11.2: Matter Waves (de Broglie Hypothesis)

21.

(MCQ) The hypothesis that moving material particles possess a wave-like character was first proposed by:

(a) Albert Einstein

(b) Max Planck

(d) Niels Bohr

22.

(MCQ) The formula for the de Broglie wavelength ($\lambda$) of a particle of mass $m$ moving with velocity $v$ is:

(a) $\lambda = \frac{h}{mv}$

(b) $\lambda = \frac{mv}{h}$

(d) $\lambda = \frac{h^2}{mv}$

23.

(MCQ) What is the relationship between momentum ($p$) and kinetic energy ($K$) for a non-relativistic particle of mass $m$?

(a) $p = \sqrt{mK}$

(b) $p = \sqrt{2mK}$

(d) $p = mK^2$

24.

(Fill in the blank) The waves intrinsically associated with moving material particles are termed ____________ waves.

25.

(Fill in the blank) According to de Broglie, the wavelength of an object is ____________ proportional to its momentum.

26.

(True/False) Matter waves are electromagnetic in nature.

27.

(True/False) A heavy car moving at $50 \text{ km/h}$ has a measurable and observable de Broglie wavelength.

28.

(One Word) For an electron accelerated through a potential difference of $V$ volts, its kinetic energy $K$ becomes numerically equal to ____________.

29.

(Formula) Write the formula for the de Broglie wavelength $\lambda$ in terms of kinetic energy $K$ and mass $m$.

30.

(MCQ) For an electron accelerated from rest through a potential $V$, the direct formula for its de Broglie wavelength (in Angstroms) is:

(a) $\frac{1.227}{\sqrt{V}} \text{ \AA}$

(b) $\frac{12.27}{\sqrt{V}} \text{ \AA}$

(d) $\frac{0.1227}{\sqrt{V}} \text{ \AA}$

31.

AI Image Prompt: A clean, high-quality, mathematically correct landscape graph plotting the de Broglie wavelength (lambda) on the y-axis against the term (1/sqrt(V)) on the x-axis for an accelerated electron. The graph must strictly show a straight line passing through the origin, demonstrating direct proportionality. The background of the whole image should be fully white.

Filename: Level0_Q31_DeBroglie_Wavelength_Graph.png

32.

(Fill in the blank) As the mass of a particle increases, its de Broglie wavelength strictly ____________ (assuming velocity is constant).

33.

(Fill in the blank) The magnitude of momentum for a photon of wavelength $\lambda$ is $p = $ ____________.

34.

(True/False) A proton and an electron possessing the exact same kinetic energy will have identical de Broglie wavelengths.

35.

(True/False) The rest mass of a photon is zero.

36.

(Match the following A to D with 1 to 4)

A. Light showing interference	1. Particle nature of light
B. Photoelectric effect	2. Matter wave equation
C. $\lambda = h/p$	3. Wave nature of light
D. Rest mass of photon	4. Exactly Zero

37.

(One Word) What do we call the fundamental physical principle stating that radiation and matter possess both wave-like and particle-like characteristics? (____________ Nature).

38.

(One Word) In the formula $\lambda = h/p$, what physical property does $p$ represent?

39.

(Formula) Write the equivalent momentum equation for a photon if its frequency $\nu$ and the speed of light $c$ are known.

40.

(Formula) Write the formula for the kinetic energy ($K$) of a particle in terms of its momentum ($p$) and mass ($m$).

Topic 11.3: Davisson-Germer Experiment

41.

AI Image Prompt: A clean, high-quality, mathematically correct landscape schematic diagram of the Davisson-Germer experimental setup. It must clearly show an Electron Gun emitting a beam, a Nickel (Ni) target crystal, and a movable circular Electron Detector (Faraday Cylinder) collecting scattered electrons. Include angular labels for the scattering angle. The background of the whole image should be fully white.

Filename: Level0_Q41_Davisson_Germer_Setup.png

42.

(MCQ) The Davisson-Germer experiment provided the first experimental verification of the:

(a) Particle nature of light

(b) Wave nature of electrons

(d) Photoelectric effect

43.

(MCQ) The target crystal utilized to violently scatter the electron beam in the Davisson-Germer setup was made of:

(a) Copper

(b) Silicon

(d) Gold

44.

(MCQ) In the famous result, a sharp pronounced intensity peak in electron scattering was observed at an accelerating voltage of:

(a) $44 \text{ V}$

(b) $54 \text{ V}$

(d) $100 \text{ V}$

45.

(Fill in the blank) The sharp intensity peak at $54 \text{ V}$ occurred at a specific scattering angle of $\phi = $ ____________ degrees.

46.

(Fill in the blank) The phenomenon responsible for the sharp intensity peaks of scattered electrons is called constructive ____________.

47.

(True/False) The Davisson-Germer experiment relied on the diffraction of electrons from the atomic planes of a crystal lattice.

48.

(True/False) The theoretical de Broglie wavelength for a $54 \text{ V}$ electron perfectly matched the experimental wavelength derived using Bragg's law.

49.

(One Word) What is the name of the cylindrical device used in the experiment to detect the intensity of scattered electrons at various angles? (Faraday ____________).

50.

(Formula) Write Bragg's Law equation relating interplanar spacing ($d$), glancing angle ($\theta$), and wavelength ($\lambda$) for the first-order diffraction ($n=1$).

51.

AI Image Prompt: A clean, high-quality, mathematically correct landscape polar graph of the Davisson-Germer experimental results. It must show a pronounced 'bump' or lobe (intensity peak) at exactly a 50-degree scattering angle. Label the accelerating voltage explicitly as 54V. The background of the whole image should be fully white.

Filename: Level0_Q51_Davisson_Germer_Polar_Graph.png

52.

(Fill in the blank) In the experimental setup, electrons are thermionically emitted from a heated ____________ filament.

53.

(Fill in the blank) The theoretical de Broglie wavelength of an electron accelerated through $54 \text{ V}$ is approximately ____________ $\text{\AA}$ (Angstroms).

54.

(True/False) A low-tension (L.T.) battery is utilized in the circuit to accelerate the electron beam towards the target.

55.

(True/False) The Davisson-Germer experiment proved that matter waves behave similarly to X-rays undergoing Bragg diffraction in crystals.

56.

(Match the following A to D with 1 to 4)

A. Filament	1. Accelerates electrons
B. High Tension (H.T.) Battery	2. Emits electrons by heating
C. Nickel Crystal	3. Detects electron intensity
D. Movable Collector	4. Diffracts the electron beam

57.

(One Word) In the relation $\theta + \phi/2 = 90^\circ$ used for the experiment, what does $\phi$ stand for? (____________ Angle).

58.

(One Word) What physical property of the electron beam does the galvanometer attached to the Faraday cylinder actually measure? (____________).

59.

(Formula) Write the formula to find the glancing angle ($\theta$) if the scattering angle ($\phi$) is known for the normal incidence setup.

60.

(One Word) Was the entire Davisson-Germer experiment conducted in air or in a vacuum chamber?

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