Question

Problem 2: Helium Spectra In helium, there are two electrons, which makes the math in finding their energy levels much more complicated. As a first approximation to that math, we can use Bohr energy levels with Z = 1.34 for the neutral helium atom (ie when both electrons are present), and Z = 2 for the singly ionized helium atom (ie when only one electron is present). The lower Z value for the neutral helium atom can be thought of as the first electron is 'shielding' the two protons in the nucleus, so there's an effectively lower number of protons. a) What wavelength (and color) of light ionizes neutral helium, where the electron is in the n = 3 excited state? Hint: ionizing means the electron is removed from the atom, n = 0, b) What wavelength (and color) of light ionizes singly ionized helium, where the electron is in the n= 5 excited state? c) What wavelength (and color) of light takes the electron in singly ionized helium, and raises it from n = 4 ton = 6? Recall energy levels in the Bohr model are given by E, = - 13.62/n, where E, is in eV.

Answer 1

Ene - 13.6 2 ² 2=1034 for neutral Helium DE = o ( n-4 for 3rd DE = 13.6+1+34) en aho DE = ** = 6.62X Dº Xxnn 1.xloky I DE 12400 ev - (2 (4) 12400 - 8124. A 136x (134) infrared

Date : 1 (b) Singly ionized the Z=2 5 hexuled A E Ex- E stet net DE = (13-6x (2) 2 en ako DE = hea 12400 Dunn de 6² x 12 400 - 13.6 x 22 . Az 820508 & infrared Co. m = u n26 sungly ionized ДЕЕ. — Eu The 13.672 13.6 z ² ex 12400 = 13.6 x (2) 2 ( 11 - 1 az 12 400 x 16x36 13.6 x 4 x 20 a = 6564 7 4 orange (62 42 Redlight