Electron Scattering Quiz

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Questions and Answers

What property of a photon indicates that it cannot exist at rest?

It travels slower than light.

It has zero rest mass. (correct)

It can exist in multiple states.

It has a finite mass.

Which equation represents the energy of a photon?

E = hν (correct)

E = h/λ

E = mc^2

E = p/c

In the photoelectric effect, what is the term for the current constituted by emitted electrons?

Ionization current

Electric current

Photon current

Photoelectric current (correct)

What happens to the wavelength of a photon when it travels from one medium to another?

It can change depending on the medium. Signup and view all the answers

Which of the following is NOT a type of light energy that can cause the photoelectric effect?

Radio waves Signup and view all the answers

What is the speed of a photon in a vacuum?

3 x 10^8 m/s Signup and view all the answers

Which property of photons allows them to show diffraction?

Wavelength variation Signup and view all the answers

In the context of the photoelectric effect, what is the role of frequency?

It influences the emitted current's intensity. Signup and view all the answers

What factor does not affect the stopping potential in the photoelectric effect?

Intensity of incident light Signup and view all the answers

How does the photoelectric current behave with increasing positive potential applied to the anode?

It increases to a saturation point Signup and view all the answers

What occurs to the photoelectric current when the potential is taken below zero?

It decreases to zero Signup and view all the answers

What is the threshold frequency in the context of photoelectric emission?

The minimum frequency needed for emission Signup and view all the answers

How is the saturation current related to the frequency of incident light?

It is the same for different frequencies Signup and view all the answers

Which of the following statements is true regarding the photoelectric current?

It is directly proportional to intensity above threshold frequency Signup and view all the answers

What determines the threshold frequency for a given material?

The nature of the metal emitting photoelectrons Signup and view all the answers

What relationship does stopping potential have with frequency?

Stopping potential increases with increased frequency Signup and view all the answers

At which scattering angle is the intensity of the scattered beam of electrons maximized?

50° Signup and view all the answers

What is the accelerating potential from the electron gun when the scattered intensity is maximum?

54 V Signup and view all the answers

Which equation relates the lattice spacing, angle of scattering, and the wavelength of the beam?

Bragg's Equation Signup and view all the answers

What is the lattice spacing for the nickel crystal mentioned?

0.91 Å Signup and view all the answers

Using de Broglie’s hypothesis, what is the calculated wavelength for an electron moving at 54 V?

1.67 Å Signup and view all the answers

What is the value of the lattice spacing when using the first principal maximum (n = 1) in the context of Bragg's equation?

1.65 Å Signup and view all the answers

What overall trend is observed for the intensity of the scattered beam of electrons as the accelerating potential increases?

Increases until a maximum then decreases Signup and view all the answers

Which principle states that electron diffraction is similar to X-ray diffraction?

Wave-particle duality Signup and view all the answers

What happens to the maximum kinetic energy of photoelectrons when the frequency of incident light is increased?

It increases proportionally. Signup and view all the answers

Which factor does NOT affect the maximum kinetic energy of the photoelectrons?

Intensity of incident light. Signup and view all the answers

What is the role of the work function in the photoelectric effect?

It is the energy needed to remove an electron from the surface of the metal. Signup and view all the answers

How does the rate of photoelectron emission relate to the intensity of light?

It is directly proportional to the intensity. Signup and view all the answers

What determines the emission of a photoelectron from a metal surface?

The frequency of the incident light must be above the threshold frequency. Signup and view all the answers

Which statement best describes the photoelectric emission process?

One photon results in the emission of one electron. Signup and view all the answers

According to Einstein's photoelectric equation, what is the equation for maximum kinetic energy (K.E.) of the emitted photoelectron?

$K.E. = h (ν - ν0)$ Signup and view all the answers

What condition results in a negative maximum kinetic energy of the photoelectron?

When the frequency is less than the threshold frequency. Signup and view all the answers

How does the de Broglie wavelength relate to the velocity of a particle?

It is inversely proportional to the velocity. Signup and view all the answers

What happens to the de Broglie wavelength of a particle when it is at rest?

It becomes infinite. Signup and view all the answers

How is the de Broglie wavelength affected by the mass of a particle?

It is inversely proportional to the mass. Signup and view all the answers

What type of waves are described as matter waves?

Probability waves representing the likelihood of a particle's existence. Signup and view all the answers

In the equation $ u = \frac{hc}{\lambda}$, what does $ u$ represent?

Frequency of the photon. Signup and view all the answers

What is the significance of the Davisson and Germer experiment?

It provided evidence for the wave nature of electrons. Signup and view all the answers

If a particle increases in mass, what effect does it have on its de Broglie wavelength?

The wavelength decreases. Signup and view all the answers

Which statement about matter waves is incorrect?

They exhibit mechanical wave properties. Signup and view all the answers

Study Notes

Electron Diffraction and Crystal Lattice

The energy of the incident electron beam is adjustable by altering the voltage of the electron gun.
Maximum intensity of scattered electrons occurs at a scattering angle of 50° and an accelerating voltage of 54 V.
Lattice spacing for nickel (Ni) crystal is 0.91 Å, used in diffraction calculations.
Bragg’s equation (2d\sin\theta = n\lambda) yields a wavelength (λ = 1.65 Å) for the first principal maximum ((n = 1)).
de Broglie wavelength for an electron at 54 V is approximately 1.67 Å, aligning closely with the value derived from diffraction.

Photons and Their Properties

A photon is defined as a packet or bundle of energy, with energy given by (E = h\nu) (Planck's constant (h), frequency (\nu)).
Photons travel at light speed (c) (approx. (3 \times 10^8 m/s)) and possess zero rest mass, meaning they cannot exist at rest.
Kinetic mass of a photon relates to its energy (E) and wavelength (λ) through the equation (m = \frac{E}{c^2} = \frac{h}{cλ}).
Photons have momentum expressed as (p = \frac{E}{c} = \frac{h}{λ}) and travel in straight lines.
Photon energy is frequency-dependent, while wavelength changes in different media; photons are electrically neutral.

Photoelectric Effect

The photoelectric effect involves the emission of electrons from metal surfaces when exposed to suitable light (including X-rays, UV light).
The emitted electrons are termed photoelectrons, and their collective movement is classified as photoelectric current.
Nonmetals, liquids, and gases can also exhibit the photoelectric effect, albeit to a lesser extent.

Effects of Intensity and Frequency on Photoelectric Current

The photoelectric current depends on the number of emitted photoelectrons, which correlates to photon incidence rather than their energy.
For fixed light intensity, increasing the anode's positive potential leads to a saturation current that remains consistent across incident light frequencies.
The photoelectric current diminishes below the threshold frequency, vital for emission, which varies by metal type.

Threshold Frequency and Laws of Photoelectric Emission

The threshold frequency represents the minimum frequency required for photoemission, independent of light intensity.
The number of emitted photoelectrons correlates directly with light intensity, given frequency exceeds the threshold.
Maximum kinetic energy of emitted electrons is proportional to the frequency, not intensity.
Photoelectric emission occurs instantaneously upon photon incidence and follows a one-to-one interaction model.

Einstein’s Photoelectric Equation

The energy of a photon (hν) translates into overcoming a work function (\Phi) and imparting kinetic energy to an electron:
- (hν = Φ + \frac{1}{2}mv_{max}^2).
The equation confirms that for photon energy below a threshold ((\nu < ν_0)), photoelectric emission cannot occur.

De Broglie Wavelength and Matter Waves

The de Broglie wavelength equation is (\lambda = \frac{h}{mv}).
Wavelength inversely correlates with particle velocity, suggesting faster particles have shorter wavelengths.
Resting particles have infinite de Broglie wavelengths, which are non-visualizable.
Heavier particles exhibit shorter de Broglie wavelengths compared to lighter counterparts.
Matter waves are distinct from electromagnetic waves, classified as probability waves that indicate the likelihood of particle positioning.

Davisson and Germer Experiment

Conducted by directing a beam of electrons at a nickel crystal oriented along a cubical axis, demonstrating electron diffraction patterns and verifying wave-particle duality principles.

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Description

This quiz explores the principles of electron scattering, focusing on the relationship between the energy of the electron beam and the scattering angles. Specifically, it examines scenarios including varying applied voltages and optimal angles of scattering, such as the maximum intensity at 50°. Test your understanding of electron behavior in crystal lattices.