Q: A metal has a threshold frequency of $$4.60 \times 10$$^{14}$$\ \mathrm{s}^{-1}. $$What is the minimum energy required to eject an electron from this metal? (Planck's constant $$h = 6.626 \times 10$$^{-34}$$\ \mathrm{J \cdot s})$$

$$3.05 \times 10$$^{-19}$$\ \mathrm{J}$$

Q: According to de Broglie's hypothesis, what is the wavelength of an electron (mass $$9.11 \times 10$$^{-31}$$\ \mathrm{kg}) $$moving at $$2.65 \times 10^6$\ \mathrm{m/s}$$? (Planck's constant $$h = 6.626 \times 10$$^{-34}$$\ \mathrm{kg \cdot m^2$/s})$$

$$2.74 \times 10$$^{-10}$$\ \mathrm{m}$$

Question 1

Which experimental observation led to the development of the quantum theory of light?

Accepted Answer

The emission of electrons from a metal surface only when light of a certain minimum frequency shines on it.

Question 2

According to the photoelectric effect, what happens if light with a frequency below the threshold frequency shines on a metal surface?

Accepted Answer

No electrons are ejected, regardless of the light's intensity.

Question 3

Which equation correctly relates the energy of a photon to its frequency?

Accepted Answer

$$E = h 
u$$

Question 4

A metal has a threshold frequency of $$4.60 	imes 10$$^{14}$$\ \mathrm{s}^{-1}. $$What is the minimum energy required to eject an electron from this metal? (Planck's constant $$h = 6.626 	imes 10$$^{-34}$$\ \mathrm{J \cdot s})$$

Accepted Answer

$$3.05 	imes 10$$^{-19}$$\ \mathrm{J}$$

Question 5

Which statement best describes the emission spectrum of an element?

Accepted Answer

It consists of discrete lines corresponding to specific wavelengths emitted by the element.

Question 6

According to de Broglie's hypothesis, what is the wavelength of an electron (mass $$9.11 	imes 10$$^{-31}$$\ \mathrm{kg}) $$moving at $$2.65 	imes 10^6$\ \mathrm{m/s}$$? (Planck's constant $$h = 6.626 	imes 10$$^{-34}$$\ \mathrm{kg \cdot m^2$/s})$$

Accepted Answer

$$2.74 	imes 10$$^{-10}$$\ \mathrm{m}$$

Question 7

Which of the following best explains why electrons in atoms do not have definite paths, according to quantum mechanics?

Accepted Answer

The Heisenberg uncertainty principle states that position and velocity cannot both be known exactly.

Question 8

What is the principal quantum number $$n$$ primarily associated with?

Accepted Answer

The energy and size of the orbital.

Question 9

How many possible values of the magnetic quantum number $$m_l$$ are there for $$l = 2$$?

Accepted Answer

5

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 shape of an atomic orbital?

Accepted Answer

Angular momentum quantum number $$l$$

Question 12

How many orbitals are present in the $$n = 3$$ energy level of an atom?

Accepted Answer

9

Question 13

Which of the following statements about the photoelectric effect is correct?

Accepted Answer

Increasing the intensity of light below the threshold frequency does not cause electron emission.

Question 14

If a photon has a wavelength of $$500\ \mathrm{nm}$$, what is its energy? (Planck's constant $$h = 6.626 	imes 10$$^{-34}$$\ \mathrm{J \cdot s}$$, speed of light $$c = 3.00 	imes 10^8$\ \mathrm{m/s})$$

Accepted Answer

$$3.98 	imes 10$$^{-19}$$\ \mathrm{J}$$

Question 15

Which quantum number(s) are needed to uniquely identify an orbital in an atom?

Accepted Answer

Principal quantum number $$n$$, angular momentum quantum number $$l$$, and magnetic quantum number $$m_l$$

Question 16

Which of the following best describes the relationship between the energy of an electron in a hydrogen atom and the principal quantum number $$n$$?

Accepted Answer

The energy becomes less negative (closer to zero) as $$n$$ increases.

Question 17

Which of the following is a correct set of possible quantum numbers for a $$3d$$ orbital?

Accepted Answer

$$n = 3,\ l = 2,\ m_l = 1$$

Question 18

Which statement about the uncertainty principle is correct?

Accepted Answer

It states that the product of the uncertainties in position and velocity is greater than or equal to a constant.

Question 19

How many sublevels are present in the $$n = 4$$ principal energy level?

Accepted Answer

4

Question 20

Which of the following best describes the complementary nature of the wave and particle properties of electrons?

Accepted Answer

Observing the wave nature prevents simultaneous observation of the particle nature, and vice versa.

The Quantum-Mechanical Model of the Atom: Wave-Particle Duality and Atomic Structure

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