The following three problems are about the following situation: You will be give

Question

The following three problems are about the following situation: You will be given an element in its ground state energy level. Determine what is a possible set of quantum numbers (n, l, ml, ms) for the outer electron.

9)  Helium

a)(1, 0, 0, +1/2)

b)(1, 1, 0, +1/2)

c)(1, 0, 1, +1/2)

d)(1, 1, 0, -1/2)

e)(1, 0, 1, -1/2)

10)  Oxygen

a)(2, 0, 1, +1/2)

b)(2, 0, 1, -1/2)

c)(2, 1, -1, +1/2)

d)(2, 0, -1, +1/2)

e)(2, 0, -1, -1/2)

11)  Calcium

a)(3, 1, 0, +1/2)

b)(3, 1, 1, +1/2)

c)(4, 2, 0, +1/2)

d)(4, 2, 1, +1/2)

e)(4, 0, 0, +1/2)

15)  A hydrogen atom in the ground state absorbs energy and makes a transition to the n = 3 state. The atom returns to the ground state by emitting two photons. What are the wavelengths of the two photons?

a)6.56 x 10-7m, 1.22 x 10-7m

b)6.56 x 10-7m, 5.45 x 10-7m

c)3.43 x 10-7m, 1.22 x 10-7m

d)5.45 x 10-7m, 3.43 x 10-7m

Explanation / Answer

9) a)(1, 0, 0, +1/2)

10) c)(2, 1, -1, +1/2)

11) e)(4, 0, 0, +1/2)

15) The transition has to go n = 3 -> n=2 then n=2 ->n=1

The energy of the photons is

E32 = -13.6 eV*(1/3^2 - 1/2^2) = 1.889 eV

E21 = -13.6eV(1/2^1 -1/1) = 10.2 eV

Now E = hc/l for a photon where h= planck's constant, c = speed of light and l = wavelength

1 eV = 1.6 x 10^-19 J

So l32 = hc/E32 = 6.62x10^034*3x10^8/(1.6x10^-19*1.889) = 6.56 x 10^-7 m

l21 = hc/E21 = 1.22x10^-7 m

ans a)6.56 x 10-7m, 1.22 x 10-7m

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