Q: A 4.003 amu helium atom is moving at 125 m/s. What is its kinetic energy in joules? (1 amu = $$1.66054 \times 10$$^{-27}$$ kg)

$$E_k = \frac{1}{2}mu^2$ = \frac{1}{2} \times 4.003 \times 1.66054 \times 10$$^{-27}$$ \text{ kg} \times (125 \text{ m/s})^2$ = 5.19 \times 10$$^{-23}$$ \text{ J}$$

Q: A laser used in medical treatments emits light at 532 nm. What is the frequency of this radiation? ($$c = 3.00 \times 10^8$ m/s)

$$\nu = \frac{c}{\lambda} = \frac{3.00 \times 10^8$}{532 \times 10$$^{-9}$$} = 5.64 \times 10$$^{14}$$ \text{ Hz}$$

Q: A photon with a wavelength of 52 nm strikes a metal with a binding energy of 3.7 eV. What is the maximum kinetic energy of the ejected electron? ($$h = 6.626 \times 10$$^{-34}$$ J·s, c = 3.00$$ \times $$10^8 m/s$$, $$1 \text{ eV} = 1.602 \times 10$$^{-19}$$ J)

$$E_{photon} = \frac{hc}{\lambda} = \frac{6.626 \times 10$$^{-34}$$ \times 3.00 \times 10^8$}{52 \times 10$$^{-9}$$} = 3.82 \times 10$$^{-18}$$ \text{ J}$$; $$E_{binding} = 3.7 \times 1.602 \times 10$$^{-19}$$ = 5.93 \times 10$$^{-19}$$ \text{ J}$$; $$KE = 3.82 \times 10$$^{-18}$$ - 5.93 \times 10$$^{-19}$$ = 3.23 \times 10$$^{-18}$$ \text{ J}$$

Question 1

Which of the following statements best describes the law of conservation of energy as it applies to chemical reactions?

Accepted Answer

Energy can neither be created nor destroyed; it can only change forms during a chemical reaction.

Question 2

A 4.003 amu helium atom is moving at 125 m/s. What is its kinetic energy in joules? (1 amu = $$1.66054 	imes 10$$^{-27}$$ kg)

Accepted Answer

$$E_k = \frac{1}{2}mu^2$ = \frac{1}{2} 	imes 4.003 	imes 1.66054 	imes 10$$^{-27}$$ 	ext{ kg} 	imes (125 	ext{ m/s})^2$ = 5.19 	imes 10$$^{-23}$$ 	ext{ J}$$

Question 3

If the attraction between charges of +2 and −2 is compared to that between +1 and −1 at the same distance, how much greater is the attraction?

Accepted Answer

Four times as large

Question 4

Which equation correctly relates the speed of light ($$c$$), wavelength ($$\lambda$$), and frequency ($$
u$$)?

Accepted Answer

$$c = \lambda 
u$$

Question 5

A laser used in medical treatments emits light at 532 nm. What is the frequency of this radiation? ($$c = 3.00 	imes 10^8$ m/s)

Accepted Answer

$$
u = \frac{c}{\lambda} = \frac{3.00 	imes 10^8$}{532 	imes 10$$^{-9}$$} = 5.64 	imes 10$$^{14}$$ 	ext{ Hz}$$

Question 6

Which experiment provided evidence for the wave nature of light by producing an interference pattern?

Accepted Answer

The double-slit experiment

Question 7

According to Planck’s quantum theory, what is the energy of a photon with frequency $$
u$$?

Accepted Answer

$$E = h
u$$

Question 8

In the photoelectric effect, what happens if the frequency of incident light is below the threshold frequency for a metal?

Accepted Answer

No electrons are ejected, regardless of the light’s intensity.

Question 9

A photon with a wavelength of 52 nm strikes a metal with a binding energy of 3.7 eV. What is the maximum kinetic energy of the ejected electron? ($$h = 6.626 	imes 10$$^{-34}$$ J·s, c = 3.00$$ 	imes $$10^8 m/s$$, $$1 	ext{ eV} = 1.602 	imes 10$$^{-19}$$ J)

Accepted Answer

$$E_{photon} = \frac{hc}{\lambda} = \frac{6.626 	imes 10$$^{-34}$$ 	imes 3.00 	imes 10^8$}{52 	imes 10$$^{-9}$$} = 3.82 	imes 10$$^{-18}$$ 	ext{ J}$$; $$E_{binding} = 3.7 	imes 1.602 	imes 10$$^{-19}$$ = 5.93 	imes 10$$^{-19}$$ 	ext{ J}$$; $$KE = 3.82 	imes 10$$^{-18}$$ - 5.93 	imes 10$$^{-19}$$ = 3.23 	imes 10$$^{-18}$$ 	ext{ J}$$

Question 10

Which of the following best explains why the emission spectrum of hydrogen consists of discrete lines?

Accepted Answer

Electrons in hydrogen atoms can only occupy specific energy levels, and transitions between these levels emit photons of specific energies.

Question 11

According to Bohr’s model, what happens when an electron in a hydrogen atom moves from $$n=4 to$$ $$n=2$$?

Accepted Answer

A photon is emitted with energy equal to the difference between the two energy levels.

Question 12

Which equation gives the de Broglie wavelength of a particle with mass $$m$$ and velocity $$u$$?

Accepted Answer

$$\lambda = \frac{h}{mu}$$

Question 13

Which principle states that it is impossible to know both the exact position and momentum of a particle simultaneously?

Accepted Answer

Heisenberg uncertainty principle

Question 14

Which quantum number determines the shape of an atomic orbital?

Accepted Answer

Angular momentum quantum number ($$l)$$

Question 15

How many possible values of the magnetic quantum number ($$m_l) $$are there for a 4d subshell?

Accepted Answer

Five: $$-2, -1, 0, +1, +2$$

Question 16

Which of the following statements about s, p, and d orbitals is correct?

Accepted Answer

All s orbitals are spherical, p orbitals are dumbbell-shaped, and d orbitals have more complex shapes.

Question 17

In the hydrogen atom, the energy of an orbital depends on which quantum number(s)?

Accepted Answer

Only the principal quantum number ($$n)$$

Question 18

Which quantum number is responsible for the orientation of an orbital in space?

Accepted Answer

Magnetic quantum number ($$m_l)$$

Quantum Theory and the Electronic Structure of Atoms: Study Notes

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