# Spectrum, Quantum Numbers, and Orbital Shapes

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}

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#### Solution Preview

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 ...

#### Solution Summary

Answers questions on Spectrum, Quantum Numbers, Orbital Shapes.

Chemistry: Orbitals and Electron Configurations, deBroglie Wavelengths

The following 5 problems concern electron configuration, the shape of orbitals, and calculation of Bohr wavelengths. Please see the attached file for the fully formatted problems.

1. A hydrogen atom in a certain excited state has its electron in a 5f subshell. The electron drops down to the 3d subshell, releasing a photon in the process.

a) For each of these subshells. Give the n and 1 quantum numbers, and give the range of possible ml quantum numbers.

b) How many radial nodes and how many angular nodes does each of the orbitals in part a) have?

c) Determine the wavelength of light that would be emitted by this process.

d) The hydrogen atom now has a single electron in the 3d subshell. Calculate the energy (in kJ/mol) required to ionize this (excited state) hydrogen atom. This is the energy required to remove the electron completely from the atom.

2.

a) Write the ground-state electron configuration and count the number of unpaired electrons in cesium.

b) The photoelectric binding energy of cesium is 183.7 kJ/mol. Light having a wavelength of 2.4 x iO in falls upon a cesium surface in an evacuated tube. Calculate the minimum deBroglie wavelength of the emitted photoelectrons.

3. For each of the following orbitals, provide a perspective sketch of the orbital in the Cartesian x, y, z coordinate system. Determine the number of angular nodes and the number of radial nodes in the orbital, and describe where those nodes fail. (For instance. the 2Px orbital has an angular node in the yz-plane.)

a) 1s b) 3px c) 3dx2-y2 d) 3dxz

4. Write the ground-state electron configuration and count the number of unpaired electrons in:

Si, Ni, Ir, and Gd

5. Identify the atom or ion corresponding to each of the following descriptions:

a) An atom with ground-state electron configuration [Kr]4d105s25p1

b) An atom with ground-state electron configuration [Xe]4f 145d66s2

c) An ion with charge ?2 and ground-state electron configuration [Ne]3s23p6

d) An ion with charge +4 and ground-state electron configuration [Ar]3d3