Application to an Electron Beam

This shows that the electron is equally likely to be anywhere along the X axis. In other words, the position of the electron is unknown, and the uncertainty in its position. Ax, is equal to the path length L, which is very large compared to the wavelength of the electron. On the other hand, the momentum of the electron is known fairly precisely. The value is given by the equation  

Since the value of k can be determined to quite a high accuracy, the uncertainty in the momentum is very small. This is the normal situation with an electron beam, where there is a constant flux of electrons of known energy, but the actual position of individual electrons within the beam is unknown and is of no practical interest. For this situation. Ax is very large and Ap is very small, and the product of the two must be greater than W2. 

Q A beam of electrons travels with a velocity of 1(X)0 0.01 m s. In terms of the uncertainty principle, how precisely can the position of an electron in the beam be defined at any instant  

the uncertainty in the position of the electron is given by the expression  

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