Wave Nature and Compton Effect

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Questions and Answers

What is the wavelength of the bullet calculated in the given solution?

$1.474×10^{-15} m$

$1.474×10^{-25} m$

$1.474×10^{-5} m$

$1.474×10^{-35} m$ (correct)

How does the wavelength of the electron compare to that of the bullet?

The electron's wavelength is equal to the bullet's.

The electron's wavelength is half that of the bullet's.

The electron's wavelength is longer than the bullet's. (correct)

The electron's wavelength is shorter than the bullet's.

What is the recoil energy of the electron after a photon with an energy of 1 MeV scatters at 90°?

$1.057×10^{-13} J$ (correct)

$2.512×10^{-13} J$

$1.602×10^{-13} J$

$5.442×10^{-14} J$

What is the de-Broglie wavelength of a 2000 kg car moving at 25 m/s?

$1.324×10^{-38} m$ Signup and view all the answers

What conclusion can be drawn about the de-Broglie wavelength of the scooter compared to that of the car?

The scooter's wavelength is smaller due to mass. Signup and view all the answers

What is the value of $λ'$ after the photon scattering according to the provided formulas?

$3.66×10^{-12} m$ Signup and view all the answers

What is the energy of the scattered photon after interaction with a free electron?

$5.442×10^{-14} J$ Signup and view all the answers

What key inference can be made about the wave nature of electrons compared to bullets based on their wavelengths?

Electrons exhibit wave behavior in diffraction experiments. Signup and view all the answers

What is the correct expression for the wavelength associated with an electron moving with velocity $v$?

$λ_{e} = \frac{h}{mv}$ Signup and view all the answers

When calculating the kinetic energy of a photon scattered from a particle, which of the following formulas is used?

$K.E. = hc(\frac{1}{λ} - \frac{1}{λ'})$ Signup and view all the answers

What effect does increasing the mass of a moving particle have on its associated wavelength?

Decreases wavelength Signup and view all the answers

If the wavelength of an incident photon is $1.0872A$ and it scatters at an angle of $30°$, what is the change in wavelength?

$Δλ = 0.02427A$ Signup and view all the answers

What is the wavelength associated with a stone of mass $50g$ moving at $50m/s$?

$λ_{stone} = 2.65 × 10^{-35} m$ Signup and view all the answers

What is the relationship between kinetic energy and wavelength for an electron with a kinetic energy of $100eV$?

$λ_{e} = \frac{h}{√(2mK.E.)}$ Signup and view all the answers

For an electron, what effect does its mass have on its matter wave wavelength compared to a heavier particle?

Electrons exhibit more wave nature due to their smaller mass Signup and view all the answers

What is the de Broglie wavelength of a 10 gm object moving at 10 m/s?

6.63 × 10^{-33} m Signup and view all the answers

What is the wavelength of the scattered photon when an X-ray photon with a wavelength of 0.3 A° is scattered at an angle of 45º?

0.3071 A° Signup and view all the answers

What is the wavelength of incident X-rays when the scattered wavelength is 0.22 A° and the angle of scattering is 45º?

0.212 A° Signup and view all the answers

What is the value of the recoil electron's velocity when the wavelength of incident radiation is 1.0872 A° and the angle of scattering is 30º?

9.45 × 10^6 m/s Signup and view all the answers

Calculate the Compton shift for X-rays of wavelength 4 A° scattered at an angle of 45º.

0.007104 A° Signup and view all the answers

What is the fraction of energy lost by the photon in a collision when scattered X-rays of wavelength 4 A° are measured?

0.00177 Signup and view all the answers

What is the de Broglie wavelength of an electron with a kinetic energy of 100 eV?

1.24 × 10^{-10} m Signup and view all the answers

When given a wavelength of 1.0872 A° for incident radiation, what is the resulting wavelength after scattering at an angle of 30º?

1.09045 A° Signup and view all the answers

What is the Compton shift for an X-ray photon of wavelength 1Å scattered at an angle of 90°?

$0.02426 A$ Signup and view all the answers

What is the wavelength associated with a bullet of mass 50 grams traveling at 1000 m/s?

$0.1328 × 10^{-35} m$ Signup and view all the answers

Why is the wave nature of a bullet not revealed in diffraction experiments?

The wavelength is too small to detect. Signup and view all the answers

Calculate the energy of the scattered photon when a photon of wavelength 12nm is scattered at an angle of 90°.

$1.62 × 10^{-17} J$ Signup and view all the answers

What is the wavelength of an electron traveling at 1000 m/s?

$7.288 × 10^{-7} m$ Signup and view all the answers

For an electron accelerated through a potential difference of 144V, which of the following equations would be used to find its de-Broglie wavelength?

$λ = rac{h}{mv}$ Signup and view all the answers

What energy is imparted to the recoil electron when X-ray photons scatter from a block?

$1.9878 × 10^{-15} J$ Signup and view all the answers

What is the value of $λ'$ for a photon scattered with an angle of 90° given an initial wavelength of 1A?

$1.02427 A$ Signup and view all the answers

What is the de Broglie wavelength of an electron with an energy of 60 eV?

1.5844 A° Signup and view all the answers

How does the de Broglie wavelength of an object depend on its velocity?

Inversely proportional to its velocity Signup and view all the answers

What is the correct formula to calculate the de Broglie wavelength of an electron subjected to a potential difference?

$λ = \frac{h}{√2meV}$ Signup and view all the answers

What is the angle of deviation of the first order diffraction maxima when electrons of energy 10 KeV pass through a thin film?

6.36° Signup and view all the answers

What is the de Broglie wavelength of an object with a mass of 1 kg moving at a speed of 1 m/s?

6.626 × 10^{-34} m Signup and view all the answers

What result would be expected for the de Broglie wavelength of an electron accelerated through a potential difference of 150 V?

1.001 × 10^{-10} A° Signup and view all the answers

Which variable is important in determining the de Broglie wavelength of an electron under a potential difference?

Energy of the electron Signup and view all the answers

When calculating the de Broglie wavelength, why is it important to use SI units for mass and energy?

To ensure consistency in all calculations Signup and view all the answers

Study Notes

De Broglie Wavelength and Wave Nature

The de Broglie wavelength associated with a particle with mass m and velocity v is given by:
λ = h / (mv)

where h is Planck's constant (6.626 × 10⁻³⁴ Js)

The wavelength associated with a particle with kinetic energy E can be calculated using the equation:
λ = h / √(2 * m * E)
Inference: The wave nature of particles is revealed through diffraction experiments. The larger the wavelength, the more likely it is to exhibit wave-like properties.
Examples:
- Electrons with a wavelength of ~10⁻¹⁰ m (Angstroms) are used in electron diffraction experiments.
- The wavelength of a macroscopic object (like a bullet) is extremely small (10⁻³⁵ m) and its wave nature cannot be observed through diffraction.

Compton Effect

The Compton effect is the scattering of a photon by a charged particle, typically an electron.
The Compton shift, Δλ, is the change in wavelength of the scattered photon and is given by the formula:
Δλ = (h / m₀c) (1 - cos φ)

where (h / m₀c) is the Compton wavelength (0.024264 A°) and φ is the scattering angle.
Energy conservation: The energy of the scattered photon (E') is related to the wavelength shift through:
E = hc / λ
E' = hc / λ'

where h is Planck's constant, c is the speed of light, λ is the original wavelength and λ' is the scattered wavelength.

The energy difference between the initial and scattered photons is transferred to the recoil electron.
Kinetic energy of recoil electron: The kinetic energy (KE) of the recoil electron can be calculated as:
KE = hc (1/λ - 1/λ')

Electron Diffraction

Electrons can be diffracted by a grating, similar to light waves.
Diffraction angle: The angle of deviation (θ) for the nth-order diffraction maximum is given by:
θ = sin⁻¹ (nλ/2d)

where n is the order of the maximum (e.g., 1 for the first order maximum), λ is the de Broglie wavelength, and d is the grating spacing.

Potential Energy: The de Broglie wavelength of an electron accelerated through a potential difference (V) can be calculated using:
λ = 12.27 / √V (V is measured in volts)

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Description

Explore the concepts of de Broglie wavelength and the Compton effect in this quiz. Understand how the wave nature of particles is demonstrated through diffraction and how the scattering of photons relates to electrons. Test your knowledge on the equations and implications of these phenomena.