Advance Study Assignment: Found in the gas phase, the beryllium traction (triply

Question

Advance Study Assignment: Found in the gas phase, the beryllium traction (triply charged positive, or +3, ion), Be^3+ , has an energy level formula analogous to that of the hydrogen atom, since both species have only one electron. The energy levels of the Be^3+ ion are given by the equation En=-21001/n^2 kJ/mole n=1,2,3,. . . Calculate the energies in kJ/mole for the four lowest energy levels of the Be^3+ ion. The Atomic Spectrum of Hydrogen E1= kJ/mole E2= kJ/mole E3= kJ/mole E4 = kJ/mole One of the most important transitions for the Be^3+ ion involves a jump from the n = 2 to the n = 1 level. Delta E for this transition equals E2- E1, where these two energies are obtained as in Part (a). Find the value of delta E in kJ/mole. Find the wavelength in nm of the line emitted when this transition occurs; use Equation 4 to make the calculation. delta E = kJ/mole; lambda = nm

Explanation / Answer

1) E1 = -(21001/12) = -21001 kJ/mole

E2 = -(21001/22) = -5250.25 kJ/mole

E3 = -(21001/32) = -2333.45 kJ/mole

E4 = -(21001/42) = -1312.56 kJ/mole

2) E2-E1 = 15750.75kJ/mole = 15750.75/(6.022*1023) = 2.62*10-17 J/ion

Thus, wavelength emitted = h*c/E ; where h = Planck's constant, c = velocity of light

Thus, emitted wavelength = {(6.63*10-34)*(3*108)}/2.62*1017) = 7.604*10-9 m = 7.604 nm

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