Explain what physicists mean when they say that the de Broglie wavelength relates to the probability...

Explain what physicists mean when they say that the de Broglie wavelength relates to the probability distribution wave function. Please be specific and do not copy and paste previous answers.

Expert Solution

Consider a particle having momentum . According to the wave-particle duality principle each and every object can be described by a wavepocket with a de Broglie wavelength . The momentum and wavelength are related by , where is Planck's constant. Now suppose that in a quantum measurement a particle has a uncertainty in momentum then what is the uncertainty in it's wavelength of the wavepocket or what is the spread in the wavepocket representing the object? Clearly it is which is nothing but the Heisenberg uncertaintly principle, which tells us that the product of the uncertainty in the momentum and location of an object should be always greater than . (Clearly, the concept of uncertainty means that the quantities are given by some probability distribution). In this way the de Broglie wavelength relates to the probability distribution wave function or simply the wavepocket that represents the object which we are talking about.

genius_generous answered 2 years ago

An electron has a de Broglie wavelength of 235 nm .What is the speed of the...

An electron has a de Broglie wavelength of 235 nm .What is the speed of the electron? --------------------------------------------------------------------- How much energy is contained in 1 mol of γ-ray photons with a wavelength of 2.43×10−5 nm . ? ------------------------------------------------------------------------ In a technique used for surface analysis called auger electron spectroscopy (AES), electrons are accelerated toward a metal surface. These electrons cause the emissions of secondary electrons-called auger electrons-from the metal surface. The kinetic energy of the auger electrons depends on the...

If the momentum of a particle is doubled, what happens to its de Broglie wavelength? it...

If the momentum of a particle is doubled, what happens to its de Broglie wavelength? it decreases by a factor of 2-1/2 it doubles it halves it becomes slightly less than half it slightly more than doubles

1. For what kinetic energy is the de Broglie wavelength of an electron equal to its...

1. For what kinetic energy is the de Broglie wavelength of an electron equal to its Compton wavelength? Express your answer in units of mc2 in doing the calculation, and then use mc2 = 0.5 MeV.(Answer: 0.2 MeV) 2. A beam of electrons with energy 1.0 eV approaches a potential barrier with U = 2.0 eV, whose width is 0.10 nm (see a figure below). Estimate the fraction of electrons that tunnel through the barrier. (Hint: use the relation of...

a) Derive an expression for the de Broglie wavelength of an electron in the Bohr model...

a) Derive an expression for the de Broglie wavelength of an electron in the Bohr model of the hydrogen atom as a function of a0 and n. b) Assume the uncertainty of the electron’s position is the diameter of its Bohr orbit. Derive an expression for the minimum uncertainty in electron’s velocity, (∆vn) as function of a0 and n (and other constants). c) Use quantization of angular momentum to write an expression for the velocity as a function of n,...

In this example we will apply the concept of the de Broglie wavelength to neutrons. Find...

In this example we will apply the concept of the de Broglie wavelength to neutrons. Find the speed and kinetic energy of a neutron (m=1.675×10−27kg)(m=1.675×10−27kg) that has a de Broglie wavelength λ=0.200nmλ=0.200nm, typical of atomic spacing in crystals. Compare the energy with the average kinetic energy of a gas molecule at room temperature (T=20∘C)(T=20∘C). Find the kinetic energy of an electron with a de Broglie wavelength of 0.163 nmnm .

Describe dual nature of matter? Write de Broglie wavelength and frequency? Explain the electron microscope? Write...

Describe dual nature of matter? Write de Broglie wavelength and frequency? Explain the electron microscope? Write Bohr’s theory and assumptions for hydrogen atom with energy level diagram? Write Bohr’s correspondence principle?

The mass of an electron is 9.11×10−31 kg. If the de Broglie wavelength for an electron...

The mass of an electron is 9.11×10−31 kg. If the de Broglie wavelength for an electron in a hydrogen atom is 3.31×10−10 m, how fast is the electron moving relative to the speed of light? The speed of light is 3.00×108 m/s.

The de Broglie wavelength of a proton in a particle accelerator is 1.81 × 10-14 m....

The de Broglie wavelength of a proton in a particle accelerator is 1.81 × 10-14 m. Determine the kinetic energy (in joules) of the proton.

Calculate the de Broglie wavelength of (a) a 0.715 keV electron (mass = 9.109 × 10-31...

Calculate the de Broglie wavelength of (a) a 0.715 keV electron (mass = 9.109 × 10-31 kg), (b) a 0.715 keV photon, and (c) a 0.715 keV neutron (mass = 1.675 × 10-27 kg).

2.5 Use the de Broglie relation λ=h/p to find the wavelength of electrons with kinetic energy...

2.5 Use the de Broglie relation λ=h/p to find the wavelength of electrons with kinetic energy equal to 550 eV. Indicate if relativistic or classical calculations are required. 2.3 Determine the energy of an electron and a photon if each has momentum equal to 1.071 x 10-21 kgm/s. Provide answer with 4 significant figures.ual to 550 eV. Indicate if relativistic or classical calculations are required.

Question