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Lecture15

# 2 2 2 e nx ny nz2 2m l 2 e e 211

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Unformatted text preview: ) ! 1 " N 3 Energy spacings •  What is the energy spacing between the lowest state and the next highest state for an atom free to move in a cube of volume L3? !2 " ! % 2 2 E= (nx + ny + nz2 ) \$' 2m # L & 2 !E = E (2,1,1) " E (1,1,1) !2 # " & !E = % ( [ ( 4 + 1 + 1) ) (1 + 1 + 1)] 2m \$ L ' 2 3! 2 # " & = %( 2m \$ L ' 2 Take m = mass of a 4He atom = 6.6x10 ­27 g, L= 1 cm !E = 2.48"10#37 J = 1.8"10#14 K At ﬁrst glance, you would guess that the occupancy of the ﬁrst excited state would be large even at temperatures as low as 1 mK. 4 EsUmate for μ •  The energy spli`ng: !E = 1.8 " 10 #14 K N ! 10 22 particles T ! 1 mK µ = " kT / N ! 10 "25 K μ is much closer to 0 than the 1st excited state! exp[( E (1,1,1) ! µ ) / kT ] " 1 and...
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