Problem @ Particle in a box ( quantum Nersion ) (") . . .. ESG 281 1118 / 22 We have ( see notes ) , for a particle in a box V ( -3 05 ) O X=0 . . . . we have to (x = 1a / 2 ) = 0 Cus and solutions the, = A cos( lex) or Bsin(lex) and C'I gives k = IIn n= 1, 2, 3, 4, 5.. .. a 2 and En = h 2 m a ( 1 ) Here , V - O in the box and so En is all kineticenergy . Look at the Bohr mode for H ( see notes ) TOTAL ek Epotential " - e 2 and Ekinetic for the stable orbits . r = na. .n =1 2, 3 4 . . 13.6 ev , r,= 0.529 1= 0.529 x 10 m 13. 6 ( 1 602 x 10 9 ) 5 = 2. 18 x 10-18 5 for n = 10 Skin 0.136 eV 10- 52.9A = 2. (8 x 1030a ) For nil in equation Gil , what value of a for the box will give the same value of E Kinetic for H for hit and n=10 of H ? Are these Values comparable to r, and r? 6) For a nucleus, the size of an equivalent box would be much smaller ( a nuclear size ) , Take a= lefm = (oxlonis What are Fi by and E3 ( from (1) ) Are these energies comparable to typical nuclear State energies ( " 10 - 100 Mev ) ? Take m = Mproton = 1. 673x10 -27 k