Use the energy and its uncertainty to determine wh...

Question

Use the energy and its uncertainty to determine which transitions (from initial energy level n_i to n_f) your data is consistent with.

1. E_f = 1.89e-9 eV; E_i =2.4e-9 eV

2. E_f = 1.95e-9 +/- 0.003e-9 eV; E_i = 2.51e-9 +/- 0.001e-9 eV

Patrick Ford · Accepted Answer

Change in energy:∆E=Ef-Ei[readmore]1. ∆E=1.89×10-9-2.4×10-9ΔE = - 0.51 × 10-9 eVConsidering the uncertainty relation:∆E×∆t≈ℏ2∆t=1.05×10-34(2)(0.51×10-9)(1.6×10-19)Remember: 1eV = 1.6 × 10-19 JΔt = 6.4 × 10-7 sThe transition time is 6.4 × 10-7 s.2.Ef=1.95×10-9±0.003×10-9eV={1.953×10-9eV1.947×10-9eVEi=2.51×10-9±0.001×10-9eV={2.511×10-9eV2.509×10-9eVNow we have:∆E=Ef-Ei=(1.95×10-9±0.001×10-9)-(2.51×10-9±0.001×10-9)=-0.56×10-9+(±0.003±0.001)×10-9={-0.558×10-9eV-0.562×10-9eVFrom the uncertainty relation:∆t≈ℏ2∆E={1.05×10-34(2)(0.558×10-9)(1.6×10-19)1.05×10-34(2)(0.562×10-9)(1.6×10-19)={0.588×10-6s0.584×10-6sΔt = 0.588 × 10-6 s and 0.584 × 10-6sThe transition time is 0.588 × 10-6 s and 0.584 × 10-6s.From the given two sets of data, we can conclude that the second set of data is consistent with the hydrogen atom.

Problem: Use the energy and its uncertainty to determine which transitions (from initial energy level ni to nf) your data is consistent with. 1. Ef = 1.89e-9 eV; Ei =2.4e-9 eV2. Ef = 1.95e-9 +/- 0.003e-9 eV; Ei = 2.51e-9 +/- 0.001e-9 eV

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Problem: Use the energy and its uncertainty to determine which transitions (from initial energy level ni to nf) your data is consistent with. 1. Ef = 1.89e-9 eV; Ei =2.4e-9 eV2. Ef = 1.95e-9 +/- 0.003e-9 eV; Ei = 2.51e-9 +/- 0.001e-9 eV

FREE Expert Solution

Problem Details

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