GOAL Apply the modified Bohr theory to a hydrogen-like atom.PROBLEM Singly ionized helium, He a hydrogen-like system, has one electron in the 1s orbit whenthe atom is in its ground state. Find (a) the energy of the system in the ground state in electron voltsand (b) the radius of the ground state orbit.STRATEGY Part (a) requires substitution into the modified Bohr model. In part (b) modify the equationfor the radius of the Bohr orbits by replacing e2 by Ze2, where Z is the number of protons in the nucleus.SOLUTION(A) Find the energy of the system in the ground state.Write the equation for the energies of ahydrogen-like system:Substitute the constants and convert toelectron volts:Substitute Z = 2 (the atomic numberof helium) and n = 1 to obtain theground state energy:(B) Find the radius of the ground state.Generalize to a hydrogen-like atom bysubstituting Ze2 for e²:For our case, n = 1 and Z = 2.EnEnrnm.X.2²2²2² (²2)mk 42h²E₁ = 4(13.6 eV) = -54.4 eV"1z²(13.6 eV)2n²h²mk Ze²=n²Z= 0.0265 nm-(ao)n²(0.0529 nm)LEARN MOREREMARKS Notice that for higher Z, the energy of a hydrogen-like atom is lower, which means that theelectron is more tightly bound than in hydrogen. The result is a smaller atom, as seen in part (b).QUESTION When an electron undergoes a transition from a higher to lower state in singly ionizedhelium, how will the energy of the emitted photon compare with the analogous transition in hydrogen?Explain. (Select all that apply.)The transition energy will be higher in singly ionized helium. REMARKS Notice that for higher Z, the energy of a hydrogen-like atom is lower, which means that theelectron is more tightly bound than in hydrogen. The result is a smaller atom, as seen in part (b).QUESTION When an electron undergoes a transition from a higher to lower state in singly ionizedhelium, how will the energy of the emitted photon compare with the analogous transition in hydrogen?Explain. (Select all that apply.)The transition energy will be higher in singly ionized helium.This happens because the helium atom has more protons.This happens because the helium nucleus is less massive.The transition energy will be lower in singly ionized helium.This happens because the helium atom has more neutrons.EXERCISERepeat the problem for an excited state of doubly-ionized lithium (Z = 3, n = 9).eVE2r2nmHINTS: GETTING STARTEDI'M STUCK!

We are given the doubly ionized lithium atom. This is hydrogen like atom. The energy of the nth…

Answered: EXERCISE Repeat the problem for an…

EXERCISE Repeat the problem for an excited state of doubly-ionized lithium (Z = 3, n = 9). E2= eV r2 = HINTS: GETTING STARTED nm I I'M STUCK!

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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