Q: An electron moves at $$5.97 \times 10^6$ m/s. What is its de Broglie wavelength? (m = 9.11$$ \times $$10^{-31} kg$$, $$h = 6.626 \times 10$$^{-34}$$ J·s)

$$\lambda = 1.22 \times 10$$^{-10}$$ m$

Question 1

Which statement best describes a major limitation of the Bohr model of the atom?

Accepted Answer

It fails to account for atomic bonding and periodicity.

Question 2

According to de Broglie, what is the wavelength $$\lambda of a $$particle with mass $$m$$ and velocity $$v$$?

Accepted Answer

$$\lambda = \dfrac{h}{mv}$$

Question 3

An electron moves at $$5.97 	imes 10^6$ m/s. What is its de Broglie wavelength? (m = 9.11$$ 	imes $$10^{-31} kg$$, $$h = 6.626 	imes 10$$^{-34}$$ J·s)

Accepted Answer

$$\lambda = 1.22 	imes 10$$^{-10}$$ m$

Question 4

Which equation represents Heisenberg’s Uncertainty Principle for position ($$\Delta x) $$and momentum ($$\Delta mv$$)?

Accepted Answer

$$\Delta x \cdot \Delta mv \geq \dfrac{h}{4\pi}$$

Question 5

Which quantum number determines the energy level of an electron in an atom?

Accepted Answer

The principal quantum number ($$n)$$

Question 6

For $$n = 4$$, how many subshells are present and what are their labels?

Accepted Answer

Four subshells: 4s, 4p, 4d, 4f

Question 7

What is the designation and number of orbitals for the subshell with $$n = 5$$ and $$l = 1$$?

Accepted Answer

5p, three orbitals

Question 8

Which quantum number defines the shape of an orbital?

Accepted Answer

Angular momentum quantum number ($$l)$$

Question 9

How many possible values of $$m_l$$ are there for $$l = 2$$?

Accepted Answer

Five

Question 10

Which statement about s orbitals is correct?

Accepted Answer

They are spherical and the radius increases with $$n.$$

Question 11

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

Accepted Answer

The probability density of finding an electron

Question 12

Which quantum number describes the three-dimensional orientation of an orbital?

Accepted Answer

Magnetic quantum number ($$m_l)$$

Question 13

If $$n = 4$$ and $$m_l = -1$$, what are the possible values of $$l$$?

Accepted Answer

0, 1, 2, and 3

Question 14

Which of the following best explains why quantum mechanics replaced the Bohr model?

Accepted Answer

Quantum mechanics can predict electron behavior and chemical bonding.

Question 15

What is the relationship between electron energy and the principal quantum number $$n in $$the hydrogen atom?

Accepted Answer

Energy increases as $$n$$ increases.

Question 16

Which real-world application relies on the wave nature of electrons?

Accepted Answer

Electron microscopy

Question 17

If an atom has $$n = 3$$, how many total orbitals are present in this shell?

Accepted Answer

9

Question 18

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

Accepted Answer

Principal quantum number ($$n)$$

Question 19

What is the probability of finding an electron at a node in an orbital?

Accepted Answer

Zero

Question 20

Which of the following is a correct set of quantum numbers for a 4d orbital?

Accepted Answer

$$n = 4, l = 2, m_l = 0$$

Electronic Structure of Atoms: Quantum Theory, Atomic Models, and Orbitals

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