Physics 7C FNTS due DL 8 From DL. the following equation represents the change electron energyr in a hydrogen-like atom when it transitions from some initial level 1'11- to a nal level 11):: 1 1 AE = ZZ 13.68 " ' \"(we a?) I} (challenge) a) The picture below shows the visible-light part of the emission spectrum of hot hydrogen atoms (like those in the sun). The dark sections are where there is no emission. and the four bright lines are where light emitted by the H atoms is found (the wavelengths for each line is shown below the gure}. For each line decide which energy levels (i.e.. which values of n:- and Hf) are involved. (Him: all four lines are from the same mission series: that is to say. the ending energy level (Hf) is the same for each line. For hydrogen. some of these emission series are given special names after their discoverers. The series for electrons ending in the Hf = 1 state is called the ijmn series, the series for electrons ending in the Inf 2 2 state is called the Balmer series and the series for electrons ending in the It; = 3 state is called the Pasehen series.) 410nm 434nm 486m 65611111 1:) Suppose you had cold hydrogen gas here on earth. cold enough so that all the electrons in the hydrogen atoms were in the ground state (i.e.. the state with the lowest energy). Which of the light wavelengths shown above would be absorbed by this cold hydrogen gas? 2} (challenge) Heavier elements have higher values of Z. Using the equation for the energy levels of hydrogen-like atoms given in 1). estimate where on the periodic table you start seeing x-ray emission by an element in an excited electron state (take the xray region to start at fphmn = 5 X 101? Hz}. (Note: if you look up online what is the lightest element to emit xrays. you 1will not get the right answer! This is because our model for the energy of the electrons only works for atoms with one electron. such as He'. Lil\". Be\". etc.. and real atoms are more complicated.)