Q: A sodium lamp emits yellow light with a wavelength of $$\lambda = 589\ \mathrm{nm}. $$What is the frequency $$\nu of $$this light? (Speed of light $$c = 3.00 \times 10^8$\ \mathrm{m/s})$$

$$\nu = 5.09 \times 10$$^{14}$$\ \mathrm{Hz}$$

Q: A green laser pointer emits light at $$\lambda = 532\ \mathrm{nm}. $$What is the energy of a single photon emitted by this laser? (Planck's constant $$h = 6.626 \times 10$$^{-34}$$\ \mathrm{J\cdot s}$$, $$c = 3.00 \times 10^8$\ \mathrm{m/s})$$

$$E = 3.74 \times 10$$^{-19}$$\ \mathrm{J}$$

Q: A photon has an energy of $$4.0 \times 10$$^{-19}$$\ \mathrm{J}. $$What is its wavelength? ($$h = 6.626 \times 10$$^{-34}$$\ \mathrm{J\cdot s}$$, $$c = 3.00 \times 10^8$\ \mathrm{m/s})$$

$$4.97 \times 10$$^{-7}$$\ \mathrm{m}$$

Question 1

Which of the following statements best describes the Heisenberg Uncertainty Principle?

Accepted Answer

The more precisely we know the position of a particle, the less precisely we can know its velocity.

Question 2

A sodium lamp emits yellow light with a wavelength of $$\lambda = 589\ \mathrm{nm}. $$What is the frequency $$
u of $$this light? (Speed of light $$c = 3.00 	imes 10^8$\ \mathrm{m/s})$$

Accepted Answer

$$
u = 5.09 	imes 10$$^{14}$$\ \mathrm{Hz}$$

Question 3

Which of the following transitions in a hydrogen atom emits light with the highest energy?

Accepted Answer

$$n=3 \rightarrow n=2$$

Question 4

Which quantum numbers are needed to uniquely describe an electron in an atom?

Accepted Answer

The principal quantum number $$n$$, angular momentum quantum number $$\ell$$, magnetic quantum number $$m_\ell$$, and spin quantum number $$m_s$$

Question 5

A green laser pointer emits light at $$\lambda = 532\ \mathrm{nm}. $$What is the energy of a single photon emitted by this laser? (Planck's constant $$h = 6.626 	imes 10$$^{-34}$$\ \mathrm{J\cdot s}$$, $$c = 3.00 	imes 10^8$\ \mathrm{m/s})$$

Accepted Answer

$$E = 3.74 	imes 10$$^{-19}$$\ \mathrm{J}$$

Question 6

Which of the following best explains why atoms are generally depicted as spherical in shape?

Accepted Answer

Because all the orbitals together make up a roughly spherical shape when averaged over all orientations.

Question 7

Which of the following sets of quantum numbers is NOT valid for an electron in an atom?

Accepted Answer

$$n=4,\ \ell=3,\ m_\ell=+4,\ m_s=+\frac{1}{2}$$

Question 8

Which phenomenon provides direct evidence for the wave nature of electrons?

Accepted Answer

Electron diffraction through a crystal

Question 9

A photon has an energy of $$4.0 	imes 10$$^{-19}$$\ \mathrm{J}. $$What is its wavelength? ($$h = 6.626 	imes 10$$^{-34}$$\ \mathrm{J\cdot s}$$, $$c = 3.00 	imes 10^8$\ \mathrm{m/s})$$

Accepted Answer

$$4.97 	imes 10$$^{-7}$$\ \mathrm{m}$$

Question 10

Which of the following statements about the Bohr model of the atom is correct?

Accepted Answer

Electrons occupy only certain allowed orbits with fixed energies.

Question 11

Which of the following electromagnetic radiations has the shortest wavelength?

Accepted Answer

X-rays

Question 12

How many orbitals are present in the $$n=3$$ principal energy level of an atom?

Accepted Answer

9

Question 13

Which of the following best describes constructive interference?

Accepted Answer

Waves interact so that they make a larger wave (in phase).

Question 14

A metal has a work function (binding energy) of $$\phi = 2.75\ \mathrm{eV}. $$What is the threshold wavelength $$\lambda_{	ext{th}}$$ for the photoelectric effect for this metal? ($$1\ \mathrm{eV} = 1.602 	imes 10$$^{-19}$$\ \mathrm{J}$$, $$h = 6.626 	imes 10$$^{-34}$$\ \mathrm{J\cdot s}$$, $$c = 3.00 	imes 10^8$\ \mathrm{m/s})$$

Accepted Answer

$$\lambda_{	ext{th}} = 451\ \mathrm{nm}$$

Question 15

Which of the following statements about the quantum-mechanical model of the atom is FALSE?

Accepted Answer

It states that electrons have definite paths around the nucleus.

Question 16

What is the total number of orbitals in the $$n=4$$ principal energy level?

Accepted Answer

16

Question 17

Which quantum number determines the shape of an atomic orbital?

Accepted Answer

Angular momentum quantum number $$\ell$$

Question 18

Which of the following best describes the relationship between wavelength $$\lambda$$ and frequency $$
u$$ for electromagnetic waves?

Accepted Answer

$$\lambda$$ and $$
u$$ are inversely proportional.

Question 19

Which of the following is a correct set of quantum numbers for a 5d orbital?

Accepted Answer

$$n=5,\ \ell=2,\ m_\ell=+2$$

Quantum-Mechanical Model of the Atom: Foundations and Wave Nature of Light

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