Which of the following statementsis a valid conclusion from the Heisenberg uncer

Question

Which of the following statementsis a valid conclusion from the Heisenberg uncertainty principle?

      a) Particles can exhibit wavelikebehavior.

      b) The orbits proposed by Bohr’s model of theatom are correct.

      c) An electron in a 2p orbital is always closer tothe nucleus than an electron in a 3p   orbital.

      d) The square of the wave function is proportionalto the probability of finding a particle in   space.

      e) The act of measuring a particle's positionchanges its momentum, and vice versa.

Explanation / Answer

All of these statements are correct. However, I'm not sure whichones result directly from the Heisenberg uncertainty principle - Ithink I may be mixing this up with the Shroedinger equation... Ifyou're only allowed one answer, I'd go for (e). a) Particles can exhibit wavelike behavior This is true - electrons, matter, light, etc can all show wavelikebehaviour. b) The orbits proposed by Bohr's model of the atom arecorrect Bohr's model had electrons orbiting the nucleus in defined paths.To an extent, this is true. A plot of the Shroedinger equation fora certain orbital gives an electron 'cloud', which represents thelikelihood of an electron being in a certain place (i.e. areas withlots of dots = areas where electrons are most likely to be at agiven time). If you draw a line around about 90% of these dots,this is representative of Bohr's electron orbital model. c) An electron in a 2p orbital is always closer to the nucleusthan an electron in a 3p orbital Also true. A graph of 'distance from nucleus' vs 'probability'shows that electrons of the 2p orbital are held closer to thenucleus than the 3p orbital. d) The square of the wave function is proportional to theprobability of finding a particle in space. This comes from the Shroedinger equation - the square of the wavefunction ('psi'2) gives the probability of finding theelectron in a given spot at a given time. e) The act of measuring a particle's position changes itsmomentum, and vice versa. This one I know comes from Heisenberg. The uncertainty principle isoften writen as: x*(mv) >= (h/4), wherex = uncertainty in electron position and (mv) =uncertainty in electron momentum. In other words, the product ofthe uncertainties in position and momentum must always be greaterthan (or equal to) than the constant (h/4). Therefore, if weare certain of where an electron is - that is, we decrease x- then we must become more uncertain in its momentum (increase(mv)) in order for the product to remain greater than(h/4). Hopefully I didn't confuse you too much...

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