Q: Which equation correctly represents the energy change ($$\Delta E) $$when an electron transitions from a higher energy level ($$n_i) to a $$lower energy level ($$n_f) in a $$hydrogen atom?

$$\Delta E = -2.18 \times 10$$^{-18}$$ \text{ J} \left( \frac{1}{n_f^2$} - \frac{1}{n_i^2$} \right)$$

Q: Which statement best explains why the de Broglie wavelength of a 3000-lb car moving at 60 mi/hr is undetectable?

The wavelength is extremely small ($$\sim 10$$^{-39}$$ \text{ m}$$), far below the size of atoms and beyond the detection capabilities of any instrument.

Q: If an electron is promoted from $$n = 1 to$$ $$n = 4 in a $$hydrogen atom, what is the energy required for this transition?

$$2.044 \times 10$$^{-18}$$ \text{ J}$$

Question 1

Which equation correctly represents the energy change ($$\Delta E) $$when an electron transitions from a higher energy level ($$n_i) to a $$lower energy level ($$n_f) in a $$hydrogen atom?

Accepted Answer

$$\Delta E = -2.18 	imes 10$$^{-18}$$ 	ext{ J} \left( \frac{1}{n_f^2$} - \frac{1}{n_i^2$} ight)$$

Question 2

An electron in a hydrogen atom drops from $$n = 6 to$$ $$n = 2. $$What is the wavelength of the photon emitted during this transition?

Accepted Answer

$$\lambda = 411 	ext{ nm}$$

Question 3

According to the de Broglie hypothesis, what is the formula for the wavelength ($$\lambda) of a $$moving particle?

Accepted Answer

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

Question 4

Which statement best explains why the de Broglie wavelength of a 3000-lb car moving at 60 mi/hr is undetectable?

Accepted Answer

The wavelength is extremely small ($$\sim 10$$^{-39}$$ 	ext{ m}$$), far below the size of atoms and beyond the detection capabilities of any instrument.

Question 5

Which experiment provided direct evidence for the wavelike properties of electrons?

Accepted Answer

Electron diffraction through a thin gold foil, producing concentric rings similar to X-ray diffraction.

Question 6

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

Accepted Answer

Heisenberg Uncertainty Principle

Question 7

What does the square of the wave function ($$\$$psi^2$$) represent in quantum mechanics?

Accepted Answer

The probability density of finding an electron in a particular region of space.

Question 8

How many total orbitals are associated with the principal quantum number $$n = 4$$?

Accepted Answer

16

Question 9

For $$n = 3$$, what are the possible values for the angular momentum quantum number ($$l$$)?

Accepted Answer

0, 1, 2

Question 10

Which set of quantum numbers is NOT allowed for an electron in an atom?

Accepted Answer

$$n = 2,\ l = 2,\ m_l = 0,\ m_s = +\frac{1}{2}$$

Question 11

Which quantum number determines the size of an atomic orbital?

Accepted Answer

Principal quantum number ($$n)$$

Question 12

What is the maximum number of $$d$$ orbitals in a given shell?

Accepted Answer

5

Question 13

Which statement about $$p$$ orbitals is correct?

Accepted Answer

There are three $$p$$ orbitals in each $$p$$ subshell, oriented at right angles to each other.

Question 14

If an electron is promoted from $$n = 1 to$$ $$n = 4 in a $$hydrogen atom, what is the energy required for this transition?

Accepted Answer

$$2.044 	imes 10$$^{-18}$$ 	ext{ J}$$

Question 15

Which quantum number describes the orientation of an orbital in space?

Accepted Answer

Magnetic quantum number ($$m_l)$$

Question 16

What is the relationship between the number of orbitals in a shell and the principal quantum number ($$n$$)?

Accepted Answer

Number of orbitals $$= n^2$

Question 17

Which quantum number is responsible for the two possible spin states of an electron?

Accepted Answer

Spin quantum number ($$m_s)$$

Question 18

Which of the following best describes the shape of an $$s$$ orbital?

Accepted Answer

Spherical

Question 19

What is the velocity (in $$	ext{m/s}) of an $$electron with a de Broglie wavelength of $$1.5 	imes 10$$^{-10}$$ 	ext{ m}$$?

Accepted Answer

$$4.85 	imes 10^6$ 	ext{ m/s}$$

Question 20

Which statement about the Schrödinger equation is correct?

Accepted Answer

It describes both the particle and wave behavior of electrons, but can only be solved exactly for hydrogen.

Quantum Theory and Electronic Structure of Atoms: Study Notes

Guida di studio - Domande di pratica

Study guide - Flashcard