Q: A nitrogen gas laser pulse with a wavelength of 337 nm contains 3.83 mJ of energy. How many photons does it contain? ($$h = 6.626 \times 10$$^{-34}$$ J·s, c = 3.00$$ \times $$10^8 m/s)$$

$$6.47 \times 10$$^{15}$$ photons

Question 1

Which of the following statements best describes the wave-particle duality of electrons as demonstrated by the double-slit experiment?

Accepted Answer

Electrons exhibit both wave-like and particle-like properties, producing an interference pattern similar to light waves.

Question 2

A laser emits light with a wavelength of 515 nm. What is the frequency of this light? (Speed of light $$c = 3.00 	imes 10^8$ m/s)

Accepted Answer

$$5.82 	imes 10$$^{14}$$ Hz

Question 3

Which of the following types of electromagnetic radiation has the highest energy?

Accepted Answer

X-ray

Question 4

According to the photoelectric effect, what happens when light with a frequency below the threshold frequency is shined on a metal surface?

Accepted Answer

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

Question 5

Calculate the energy of a single photon of ultraviolet light with a wavelength of 200 nm. (Planck's constant $$h = 6.626 	imes 10$$^{-34}$$ J·s, c = 3.00$$ 	imes $$10^8 m/s)$$

Accepted Answer

$$9.94 	imes 10$$^{-19}$$ J

Question 6

Which of the following sets of quantum numbers is NOT allowed for an electron in an atom?

Accepted Answer

$$n = 4;\ l = 1;\ m_l = -2$$

Question 7

Which quantum number determines the shape of an atomic orbital?

Accepted Answer

Angular momentum quantum number ($$l)$$

Question 8

A barcode scanner emits red light with a frequency of $$4.62 	imes 10$$^{14}$$ s$$^{-1}$$. What is the wavelength of this light in nanometers? (c = 3.00$$ 	imes $$10^8 m/s)$$

Accepted Answer

649 nm

Question 9

Which of the following best explains why high-energy electromagnetic radiation (such as X-rays and gamma rays) can damage biological molecules?

Accepted Answer

They have high frequencies and can ionize atoms and molecules.

Question 10

According to Heisenberg’s uncertainty principle, if the uncertainty in the position of an electron is decreased, what happens to the uncertainty in its velocity?

Accepted Answer

It increases.

Question 11

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

Accepted Answer

$$E = h
u$$

Question 12

What is the wavelength of an electron (in nm) traveling at $$2.65 	imes 10^6$ m/s? (Electron mass m = 9.11$$ 	imes $$10^{-31} kg$$, $$h = 6.626 	imes 10$$^{-34}$$ J·s)

Accepted Answer

0.273 nm

Question 13

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

Accepted Answer

Each element has a unique line spectrum because electrons transition between quantized energy levels.

Question 14

How many orbitals are present in the $$n = 3$$ principal energy level?

Accepted Answer

9

Question 15

Which of the following transitions in a hydrogen atom will emit the photon with the highest energy?

Accepted Answer

From $$n = 2 to$$ $$n = 1$$

Question 16

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

Accepted Answer

Magnetic quantum number ($$m_l)$$

Question 17

A nitrogen gas laser pulse with a wavelength of 337 nm contains 3.83 mJ of energy. How many photons does it contain? ($$h = 6.626 	imes 10$$^{-34}$$ J·s, c = 3.00$$ 	imes $$10^8 m/s)$$

Accepted Answer

$$6.47 	imes 10$$^{15}$$ photons

Question 18

Which of the following best describes the difference between the probability density function and the radial distribution function for an atomic orbital?

Accepted Answer

Probability density function gives the probability at a point; radial distribution function gives the total probability at a certain distance from the nucleus.

Question 19

Which of the following is true about the energy of an electron in a hydrogen atom as the principal quantum number $$n$$ increases?

Accepted Answer

The energy becomes less negative and the electron is less tightly bound to the nucleus.

Quantum-Mechanical Model of the Atom: Study Notes for General Chemistry

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