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# Spectrum, Quantum Numbers, and Orbital Shapes

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1. When an electrical discharged is passed through hydrogen gas, a unique four line spectrum is observed. One of the two blue wavelengths is observed at 411 nm. Calculate the frequency of this blue line. {See attachment for multiple choice options}

2. Calculate the engergy if 3 moles of photons are produced if the frequency of the second blue line in the hydrogen spectra equals {see attachment} Hz. {See attachment for multiple choice options}

3. Which of the following statments is false? {See attachment for multiple choice options}

4. How many electrons in an atom can have the following quantum numbers: {see attachment}? {See attachment for multiple choice options}

5. Which of the following oribtal shapes can be described by n = 4, f = 1? {See attachment for multiple choice options}

6. From the following list of atoms {see attachment}, select the atom that most appropriately describes the statement: {See attachment for multiple choice options}

https://brainmass.com/chemistry/modern-quantum-theory/spectrum-quantum-numbers-orbital-shapes-36565

## SOLUTION This solution is FREE courtesy of BrainMass!

1)
Answer: e )7.30 x 10^14 Hz
f = c / lambda
where
f=frequency
c = speed of light = 3x 10^8 m/s
lambda = 411 nm = 411x 10^(-9) m
Therefore f = c / lambda =(3x 10^8 m/s )/ 411x 10^(-9) m= 7.30 x 10^14 Hz

2)
Answer: e 8.27 x 10^5 Joules
E=h nu
Where
E= energy of photon
h=Planck's constant= 6.63x10^(-34) joule-sec
nu = frequency=6.91x10^14 Hz
Therefore E=h nu = 6.63x10^(-34) joule-sec x 6.91x10^14 Hz
= 4.58 x 10 ^ (-19) Joules
This is the energy of 1 photon
Energy of 3 moles of photons= 3 x (6.023 x 10^23) x 4.58 x 10 ^ (-19) Joules
=8.27 x 10^5 Joules
(1 mole = 6.023 x 10^23 particles)

3) b) is not correct because the principal quantum number only determines the overall size of the orbital and not the shape of the orbital.
a) is true because electron and proton in a hydrogen atom have opposite charges and since unlike charges attract , energy is required to move the electron away from the proton in the nucleus. Similarly c) , d) , e) and f) are true.

4)
n=3, ml = -1
For n=3 , l=1,1,2
For l=1, ml =0
For l=2, ml = -1,0,1
For l=3, ml = -2,-1,0,1,2
Therefore both l=2 and l=3 have ml = -1
For each ml , we have 2 electrons ( with opposite spin quantum numbers)
Therefore maximum no of electrons=2x2=4

n=4 , l=1 is 4 p

6) 6)
a) noble gas= Ar
b) forms a 3-ion=P
c) atom with smallest atomic radius=Ar
d) atom with the highest ionization energy=Ar
e) atom with 3 valence electrons= Al
f) metal that most easily forms a 1+ cation = Na
g) metalloid ( semi metal)=Si
h) atom with ns2 np4 electron configuration=S
i) the most positive electron affinity=Cl
j) nonmetal with the most unpaired electrons=P

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