De Broglie relationship

This equation requires the de Broglie relationship (also given in the AP exam booklet). Do not mistake a v for a V. You will also need to know J = kg m2/s2. 

The de Broglie relationship states that any beam of moving particles will display wave properties according to the formula... 

The de Broglie relationship says that the wavelength A of an object with mass m moving at a velocity v can be calculated by the equation A = h/mv. 

Neutron wavelength X is related to velocity by the de Broglie relationship A,=h/p where p=momentum=mv... 

For the problem of vibrational relaxation, the frequency of the beam is not affected when the speed is changed by application of a field (i.e. intermolecular force), and for brevity the time factor is omitted. The wavelength is 2n/k, and because of the de Broglie relationship mvX = h... 

How many values of k are there As many as the number of translations in the crystal or, alternatively, as many as there are microscopic unit cells in the macroscopic crystal. So let us say Avogadro s number, give or take a few. There is an energy level for each value of k (actually a degenerate pair of levels for each pair of positive and negative k values. There is an easily proved theorem that E(k) = E( — k). Most representations of E(k) do not give the redundant (- ), but plot ( k ) and label it as E(k)). Also the allowed values of k are equally spaced in the space of k, which is called reciprocal or momentum space. The relationship between k = 2x7 X and momentum derives from the de Broglie relationship X = hip. Remarkably, k is not only a symmetry label and a node counter, but it is also a wave vector, and so measures momentum. 

Experimental evidence was obtained by Davisson and Germer in 1927 and later by Thomson which supported the de Broglie relationship. These authors showed that crystals diffracted a beam of electrons in exactly the... 

Particularly illuminating is the free-electron MO model (FEMO) based on the assumption that Jt electrons can move freely along a one-dimensional molecular framework. Stationary states are then characterized by standing waves, and using the de Broglie relationship... 

The basis of wave mechanics is the wave equation of Schrodinger which can be obtained by the combination of the de Broglie relationship... 

An important physical observation which is a consequence of the de Broglie relationship is that electrons accelerated... 

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