Physics 1 Problem Solutions 296

Physics 1 Problem Solutions 296 - not even suspected for...

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292 Chapt. 39 Photons and Matter Waves expected the alpha particles to pass right through the foils with only small deviations. Most did, but some scattered oF a very large angles. Using a classical particle picture of the alpha particles and the entities they were scattering oF of he came to the conclusion that atoms contained most of their mass and positive charge inside a region with a size scale of 10 15 m = 1 fm: this 10 5 times smaller than the atomic size. (Note fm stands o±cially for femtometer, but physicists call this unit a fermi.) Rutherford concluded that there must be a dense little core to an atom: the nucleus. a) Why did the alpha particles scatter oF the nucleus, but not oF the electrons? HINTS: Think dense core and diFuse cloud. What is the force causing the scattering? b) If the alpha particles have kinetic energy 7 . 5 Mev, what is their de Broglie wavelength? c) The closest approach of the alpha particles to the nucleus was of order 30 fm. Would the wave nature of the alpha particles have had any eFect? Note the wave-particle duality was
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Unformatted text preview: not even suspected for the massive particles in 1911. 039 qfull 00600 2 3 0 moderate math: complex numbers Extra keywords: (HRW-977:66E) 3. A complex number z is dened by z = x + iy , where x and y are real numbers and i = 1 is imaginary. The real part of z is x = Re[ z ] and the imaginary part is y = Im[ z ] The complex conjugate of z is dened by z = x iy . a) What is zz ? b) Prove that ( z 1 z 2 ) = z 1 z 2 . c) Prove that p 1 z P = 1 z . d) Prove that p z 1 z 2 P = z 1 z 2 . 039 qfull 00700 2 5 0 moderate thinking: Schrodinger eqn. 4. Do the following. a) Verify that the full time-dependent wave function ( x,t ) = ( x ) e iEt/h reduces the full time-dependent Schrodinger equation h 2 2 m 2 x 2 + V ( x ) = ih t to the time-independent Schrodinger equation h 2 2 m 2 x 2 + V ( x ) = E...
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