Q: A photon of blue light has a wavelength of $$473\ \mathrm{nm}. $$What is its energy in joules? ($$h = 6.626 \times 10$$^{-34}$$\ \mathrm{J\cdot s}$$, $$c = 2.998 \times 10^8$\ \mathrm{m/s})$$

$$4.21 \times 10$$^{-19}$$\ \mathrm{J}$$

Question 1

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

Accepted Answer

$$c = v \lambda$$

Question 2

A photon of blue light has a wavelength of $$473\ \mathrm{nm}. $$What is its energy in joules? ($$h = 6.626 	imes 10$$^{-34}$$\ \mathrm{J\cdot s}$$, $$c = 2.998 	imes 10^8$\ \mathrm{m/s})$$

Accepted Answer

$$4.21 	imes 10$$^{-19}$$\ \mathrm{J}$$

Question 3

Which phenomenon could NOT be explained by classical physics and led to the development of quantum theory?

Accepted Answer

Blackbody radiation

Question 4

According to Planck’s quantum hypothesis, the energy of a photon is given by:

Accepted Answer

$$E = h v$$

Question 5

In the photoelectric effect, which property of light determines whether electrons are ejected from a metal surface?

Accepted Answer

Frequency

Question 6

Which transition in a hydrogen atom emits a photon with the greatest wavelength?

Accepted Answer

n=4 to n=3

Question 7

Calculate the energy (in kJ/mol) of a photon emitted when an electron in a hydrogen atom transitions from $$n=3 to$$ $$n=2$$. ($$R_y = 2.179 	imes 10$$^{-18}$$\ \mathrm{J})$$

Accepted Answer

$$164\ \mathrm{kJ/mol}$$

Question 8

Which scientist proposed that particles of matter can exhibit wavelike properties, leading to the concept of matter waves?

Accepted Answer

Louis de Broglie

Question 9

The de Broglie wavelength of a particle is given by:

Accepted Answer

$$\lambda = h / p$$

Question 10

According to Heisenberg’s uncertainty principle, which of the following is true?

Accepted Answer

The product of the uncertainties in position and momentum is always greater than or equal to $$\frac{h}{4\pi}.$$

Question 11

Which quantum number determines the shape of an atomic orbital?

Accepted Answer

Angular momentum quantum number ($$\ell)$$

Question 12

How many orbitals are present in a subshell with $$\ell = 2$$?

Accepted Answer

5

Question 13

Which set of quantum numbers is NOT allowed for an atomic orbital?

Accepted Answer

$$n=2,\ \ell=2,\ m_\ell=0$$

Question 14

Which principle states that no two electrons in an atom can have the same set of four quantum numbers?

Accepted Answer

Pauli exclusion principle

Question 15

Which electron configuration represents an excited state for carbon (C)?

Accepted Answer

$$1s^2$$\ $$2s^1$$\ $$2p^3$$

Question 16

Which of the following is the condensed electron configuration for chlorine?

Accepted Answer

$$[Ne]\ 3s^2$\ 3p^5$

Question 17

Which element has the electron configuration $$[Ar]\ 4s^2$\ 3d^1$?

Accepted Answer

Scandium (Sc)

Question 18

Which rule explains why electrons occupy degenerate orbitals singly first and with parallel spins?

Accepted Answer

Hund’s rule

Question 19

Which orbital designation corresponds to the quantum numbers $$n=3$$, $$\ell=1$$, $$m_\ell=0$$?

Accepted Answer

3p

Question 20

Which of the following statements about electron spin is correct?

Accepted Answer

Electron spin is a quantum property with two possible values: $$+\frac{1}{2}$$ and $$-\frac{1}{2}.$$

Quantum-Mechanical Model of the Atom: Electromagnetic Radiation and Historical Context

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