Q: A photon of red light has a wavelength of $650\ \mathrm{nm}$. What is its frequency? (Speed of light $c = 3.00 \times 10^8\ \mathrm{m/s}$)

$4.62 \times 10^{14}\ \mathrm{Hz}$

Question 1

Which of the following best describes the dual nature of light as discussed in quantum mechanics?

Accepted Answer

Light exhibits both wave-like and particle-like properties depending on the experiment.

Question 2

According to Planck's theory, the energy of a photon is quantized and given by which of the following equations?

Accepted Answer

$E = h 
u$

Question 3

A photon of red light has a wavelength of $650\ \mathrm{nm}$. What is its frequency? (Speed of light $c = 3.00 	imes 10^8\ \mathrm{m/s}$)

Accepted Answer

$4.62 	imes 10^{14}\ \mathrm{Hz}$

Question 4

Which experiment provided evidence for the quantization of energy and the particle nature of light?

Accepted Answer

Photoelectric effect

Question 5

According to de Broglie, what is the wavelength associated with a particle of mass $m$ moving at velocity $v$?

Accepted Answer

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

Question 6

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

Accepted Answer

Electrons move in quantized circular orbits with specific energies.

Question 7

What is the maximum wavelength (in nm) of light capable of removing an electron from the $n=4$ state in a hydrogen atom (ionization from $n=4$ to $n=\infty$)? Use $R_H = 2.18 	imes 10^{-18}\ \mathrm{J}$ and $c = 3.00 	imes 10^8\ \mathrm{m/s}$, $h = 6.626 	imes 10^{-34}\ \mathrm{J\cdot s}$.

Accepted Answer

$1459\ \mathrm{nm}$

Question 8

Which transition in the hydrogen atom emits the lowest energy photon?

Accepted Answer

$n=5 \rightarrow n=4$

Question 9

The Heisenberg Uncertainty Principle can be mathematically expressed as:

Accepted Answer

$\Delta x \cdot \Delta p \geq \frac{h}{4\pi}$

Question 10

Which quantum number primarily determines the energy of an electron in a hydrogen atom?

Accepted Answer

Principal quantum number $n$

Question 11

How many possible values of the magnetic quantum number $m_l$ are there for an $f$ orbital?

Accepted Answer

7

Question 12

Which of the following sets of quantum numbers is NOT allowed?

Accepted Answer

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

Question 13

According to the Pauli Exclusion Principle, how many electrons can occupy a single orbital?

Accepted Answer

2, with opposite spins

Question 14

Which of the following electron configurations represents a violation of the Aufbau principle?

Accepted Answer

$1s^2\ 2s^2\ 2p^6\ 3s^2\ 3p^6\ 3d^2\ 4s^2$

Question 15

Which element has the electron configuration $[\mathrm{Ar}]\ 4s^1\ 3d^{10}$, an exception to the expected order?

Accepted Answer

Copper (Cu)

Question 16

Which of the following statements about periodic trends is correct?

Accepted Answer

Ionization energy decreases down a group.

Question 17

Which quantum number determines the shape of an atomic orbital?

Accepted Answer

Angular momentum quantum number $l$

Question 18

What is the maximum number of electrons that can occupy the $3d$ subshell?

Accepted Answer

10

Question 19

Which of the following best explains why the Bohr model is still important in the history of atomic theory?

Accepted Answer

It introduced the concept of quantized energy levels for electrons.

Quantum-Mechanical Model of the Atom and Periodic Properties of the Elements

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