Question

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5) We'll find a consequence of the wave-like nature of matter is we can no longer simultaneously know the position and momentum of a particle with absolute certainty. This concept, known as the Heisenberg Uncertainty Principle, can be formulated mathematically as: where Δx and Δp are the uncertainty of the position of a particle and its linear momentum, respectively. a. In your own words, describe why a particle described by a wave should experience an inverse relationship between the uncertainty in its momentum and the uncertainty in its position If we locate an electron to within a distance given by 2πao, the circumference of the n = 1 state for Hydrogen in the Bohr model, what is our minimum uncertainty in its speed? How does this compare with the speed of an electron in the n = 1 orbit of a Bohr atom? b.

Answer 1

Let's understand this with an example if you want to measure the position of an election in an atom you will use the radiation of every shared wavelength (the size of the atom) this radiation has enough energy to change the momentum of the electron and hence it is impossible to determine the position and momentum simultaneously to arbitrary accuracy (b) for minimum uncertainly in its speed you take uncertainty in position to be maximum delta x delta P_x = hstorke/2 [minimum] delta_P_x = hstorke /2 delta x = hstorke/2 times 2 pi a_0 m delta v = hstork/4 pi a_0 delta v = hstrok/4 pi m a_0 delta v = 1.054 times 10^- 34/4 pi times 9.1 times 10^- 31 times 0.53 times 10^- 10 = 0.01739 times 10^- 34 + 31 + 10 = 0.01739 times 10^7 = 0.1739 times 10^6 m/s and speed of an electron in the n = 1