Generally useful constants (MKS):amu = 1.6605 H10^−27L kgNA = 6.02221 H10^23Lêmolek = 1.38066 H10^−23L J ê Kme = 9.1094 H10^−31L kgh = 6.62608 H10^−34L Jsq = 1.6022 H10^−19L Cc = 2.9979 H10^8L m ê s1.6605 × 10−27kg6.02221 × 1023mole1.38066 × 10−23JK9.1094 × 10−31kg6.62608× 10−34Js1.6022 × 10−19C2.9979 × 108msProblem 4.23 (Engel)A. What is the translational energy of a H2 molecule confined to a single cavity in a zeolite crystal? Treat the moleculeas if it were a single particle confined to a three-dimensional box with identical x, y, and z dimensions (1 nm on eachside) and all three quantum numbers, nx, ny, and nz= 10, respectively.B. Compare this energy to kT (or, more appropriately, kB T) at T = 300 K. Would you expect the molecule-zeolitesystem to display quantum or classical properties?Solution to Part AStrategy. From P4.19 we know (note: I have used the fact that the box has a cube shape to factor out the x, y, and zdimensions as L)EHnx, ny, nzL =h2Hnx2+ ny2+ nz2LÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅ8 mL2=h2H300LÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅ8 mL2Execution. Inserting the proper numerical values:J =kg m2s2massH2 = 2 ∗ 1.008 ∗ amuEnergy =h2 H300L8 massH2 H1 × 10−9 mL2kg m2s23.34757× 10−27kg4.9183 × 10−21kg m2s2Solution to Part BStrategy. Calculate kB T at T = 300 K. From Ch 1-2, we know that quantum effects are expected when the spacingbetween energy levels is smaller than kB T.Execution. Inserting the proper numerical values:k ∗ H300 KL4.14198 × 10−21kg m2s2This value is just slightly smaller than E(10, 10, 10) calculated above. This result is interesting, but the real question ishow this value compares to DE = E(11, 10, 10) - E(10, 10, 10).DEHnx, ny, nzL =h2@H121 + 100 + 100L - 300DÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅ8 mL2=h2H21LÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅ8 mL22P4.23.nbDelEnergy =h2 H21L8 massH2 H1×10−9 mL23.44281 × 10−22kg m2s2The energy spacing is quite a bit smaller than kB T so quantum behavior can be