2). Solar confusion: The spectral lines of the element Helium had been known, bu
ID: 3280407 • Letter: 2
Question
2). Solar confusion: The spectral lines of the element Helium had been known, but not understood, since the mid-to-late 1800’s, first from observations of the sun (hence the name “helium”) but later from measurements on Earth. Once the Bohr model had been developed, there was some confusion about some of the lines now known to come from ionized helium, which has only a single electron orbiting a Z=2 nucleus. Some observations of that spectrum suggested the (incorrect) possibility of “fractional quantization” in the hydrogen atom.
(a) (10 points) Calculate the energies of the first six transitions of the Balmer series in ionized He, and compare them to the transition energies for the first six transitions in the Lyman series for H. Identify any possible correspondences you find.
(b) (10 points) Write down a general expression that allows you to find transitions in ionized He that could be mistaken for H transitions.
Explanation / Answer
2. for balmer series of ionised helium atom
energy of transition is given by
En = hc*4*R(1/4 - 1/n^2)
where h is planks constant
c is speed of light
R is rydbergs constant = 10973731.57 m^-1
En = 2.18267*10^-18*4[1/4 - 1/n^2]
for first 6 energies of transitions, n = 3,4,5,6,7,8
E3 = 1.2125 *10^-18 J
E4 = 1.637 * 10^-18 J
E5 = 1.833*10^-18 J
E6 = 1.94*10^-18 J
E7 = 2.004*10^-18 J
E8 = 2.0462 *10^-18 J
for hydrogen, lyman series
E'n = 2.18267*10^-18[1 - 1/n^2]
so fir first 6 ernergies, n = 2,3,4,5,6,7
E'2 = 1.637*10^-18 J
E'3 = 1.9401*10^-18 J
E'4 = 2.0462*10^-18 J
E'5 = 2.0953*10^-18 J
E'6 = 2.12204*10^-18 J
E'7 = 2.1381 *10^-18 J
hence we can see
E4 = E'2
E6 = E'3
E8 = E'4
b. so, for nth energy of transition of ionised helium and mth energy of transition for ionised hydrogen
2n = m
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