Q: A small car with a mass of $$1150 \ \mathrm{kg}$$ travels at $$24.6 \ \mathrm{m/s}. $$What is its de Broglie wavelength?

$$2.34 \times 10$$^{-38}$$ \ \mathrm{m}$$

Question 1

Which fundamental property of atoms is primarily responsible for the periodic variations observed in atomic radii and other elemental characteristics?

Accepted Answer

The number of protons (atomic number)

Question 2

Which of the following correctly describes the relationship between wavelength ($$\lambda$$), frequency ($$
u$$), and the speed of light ($$c$$)?

Accepted Answer

$$c = \lambda 
u$$

Question 3

A mercury streetlamp emits light with a frequency of $$6.88 	imes 10$$^{14}$$ \ \mathrm{s}^{-1}. $$What is the wavelength of this light in nanometers?

Accepted Answer

$$\lambda = 436 \ \mathrm{nm}$$

Question 4

Which phenomenon provides evidence that light behaves as a wave?

Accepted Answer

Diffraction and interference

Question 5

According to Planck's postulate, what is the energy of a photon with frequency $$
u$$?

Accepted Answer

$$E = h 
u$$

Question 6

Which statement best describes the concept of quantized energy?

Accepted Answer

Energy is only absorbed or released in discrete packets called quanta.

Question 7

The atomic line spectrum of hydrogen can be described by the Rydberg equation. Which formula correctly expresses the wavelength of emitted light for a transition from $$n_2 to$$ $$n_1$$?

Accepted Answer

$$\dfrac{1}{\lambda} = R \left( \dfrac{1}{n_1$^2} - \dfrac{1}{n_2$^2} \right)$$

Question 8

Which of the following is NOT a basic principle of the Bohr model of the hydrogen atom?

Accepted Answer

Electrons radiate energy continuously as they move in an orbit.

Question 9

According to de Broglie’s hypothesis, what is the wavelength ($$\lambda) of a $$particle of mass $$m$$ moving at velocity $$v$$?

Accepted Answer

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

Question 10

A small car with a mass of $$1150 \ \mathrm{kg}$$ travels at $$24.6 \ \mathrm{m/s}. $$What is its de Broglie wavelength?

Accepted Answer

$$2.34 	imes 10$$^{-38}$$ \ \mathrm{m}$$

Question 11

Which statement best summarizes Heisenberg’s uncertainty principle?

Accepted Answer

It is impossible to know both the position and momentum of an electron with arbitrary precision.

Question 12

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

Accepted Answer

The probability of finding an electron in a region of space

Question 13

Which quantum number describes the size and energy level of an orbital?

Accepted Answer

Principal quantum number ($$n)$$

Question 14

For a 4p orbital, what are the possible values for the magnetic quantum number ($$m_l$$)?

Accepted Answer

$$-1, 0, 1$$

Question 15

Which set of quantum numbers is valid for an electron in a 3d orbital?

Accepted Answer

$$n=3, \ l=2, \ m_l=0$$

Question 16

How many orbitals are present in the $$n=3$$ shell?

Accepted Answer

9

Question 17

Which quantum number determines the three-dimensional shape of an orbital?

Accepted Answer

Angular momentum quantum number ($$l)$$

Question 18

Which of the following statements about atomic line spectra is correct?

Accepted Answer

Each element has a unique line spectrum that acts as a spectral signature.

Question 19

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

Accepted Answer

Magnetic quantum number ($$m_l)$$

Question 20

Which of the following best explains why the Bohr model cannot fully describe the behavior of electrons in atoms other than hydrogen?

Accepted Answer

It does not account for electron-electron interactions and fails to explain multi-electron atoms.

Atomic Structure: Light, Atomic Spectra, and Quantum Mechanical Model

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