Q: Calculate the energy required (in J) to promote an electron in a hydrogen atom from $$n=1 to$$ $$n=4. $$Use $$E_n = -2.18 \times 10$$^{-18}$$ \ \mathrm{J} \left( \frac{1}{n^2$} \right).$$

$$2.044 \times 10$$^{-18}$$ \ \mathrm{J}$$

Q: Which of the following wavelengths corresponds to the energy required to excite an electron from $$n=1 to$$ $$n=4 in a $$hydrogen atom? ($$h = 6.626 \times 10$$^{-34}$$ \ \mathrm{J\,s}$$, $$c = 3.00 \times 10^8$ \ \mathrm{m/s})$$

$$9.725 \times 10$$^{-8}$$ \ \mathrm{m}$$

Q: According to de Broglie, what is the wavelength of an electron (mass $$9.11 \times 10$$^{-31}$$ \ \mathrm{kg}) $$moving at $$2.65 \times 10^6$ \ \mathrm{m/s}$$? ($$h = 6.63 \times 10$$^{-34}$$ \ \mathrm{J\,s})$$

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

Question 1

Which of the following statements best explains why the energy of an electron in a hydrogen atom is quantized?

Accepted Answer

Because the electron can only occupy certain allowed orbits where its wavelength fits exactly into the circumference, as described by $$2\pi r = n\lambda.$$

Question 2

An electron in a hydrogen atom transitions from $$n=6 to$$ $$n=2. $$Which of the following correctly describes the process and the sign of $$\Delta E$$?

Accepted Answer

The process is exothermic and $$\Delta E is $$negative.

Question 3

Calculate the energy required (in J) to promote an electron in a hydrogen atom from $$n=1 to$$ $$n=4. $$Use $$E_n = -2.18 	imes 10$$^{-18}$$ \ \mathrm{J} \left( \frac{1}{n^2$} ight).$$

Accepted Answer

$$2.044 	imes 10$$^{-18}$$ \ \mathrm{J}$$

Question 4

Which of the following wavelengths corresponds to the energy required to excite an electron from $$n=1 to$$ $$n=4 in a $$hydrogen atom? ($$h = 6.626 	imes 10$$^{-34}$$ \ \mathrm{J\,s}$$, $$c = 3.00 	imes 10^8$ \ \mathrm{m/s})$$

Accepted Answer

$$9.725 	imes 10$$^{-8}$$ \ \mathrm{m}$$

Question 5

According to de Broglie, what is the wavelength of an electron (mass $$9.11 	imes 10$$^{-31}$$ \ \mathrm{kg}) $$moving at $$2.65 	imes 10^6$ \ \mathrm{m/s}$$? ($$h = 6.63 	imes 10$$^{-34}$$ \ \mathrm{J\,s})$$

Accepted Answer

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

Question 6

Which experiment provided direct evidence for the wave nature of electrons?

Accepted Answer

Electron diffraction through a thin gold foil, producing concentric rings.

Question 7

Which statement best summarizes the Heisenberg Uncertainty Principle?

Accepted Answer

It is impossible to simultaneously know both the exact position and exact momentum of a particle.

Question 8

The Schrödinger equation for the hydrogen atom yields solutions called wave functions ($$\psi). $$What does $$\$$psi^2$$ represent?

Accepted Answer

The probability density of finding an electron in a particular region of space.

Question 9

How many total orbitals are present in the $$n=4$$ shell of an atom?

Accepted Answer

$$16$$

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

The angular momentum quantum number $$l$$

Question 12

How many different $$d$$ orbitals are there in a given shell?

Accepted Answer

5

Question 13

Which of the following best describes the difference between a 2p and a 3p orbital?

Accepted Answer

The 3p orbital is larger and has a higher energy than the 2p orbital, but both have the same shape.

Question 14

What is the maximum number of electrons that can occupy the $$n=3$$ shell?

Accepted Answer

18

Question 15

Which of the following statements about the electron spin quantum number $$m_s is $$correct?

Accepted Answer

$$m_s$$ can have only two possible values: $$+\frac{1}{2}$$ and $$-\frac{1}{2}.$$

Question 16

A 3000-lb car travels at 60 mi/hr. What is the order of magnitude of its de Broglie wavelength?

Accepted Answer

$$10^{-39}$$ \ \mathrm{m}$$

Question 17

Which of the following is a correct statement about atomic orbitals?

Accepted Answer

An atomic orbital describes a region in space where there is a high probability of finding an electron.

Question 18

For the $$n=3$$ shell, how many total orbitals are present?

Accepted Answer

9

Question 19

Which of the following quantum numbers describes the orientation of an orbital in space?

Accepted Answer

Magnetic quantum number $$m_l$$

Question 20

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

Accepted Answer

From $$n=4 to$$ $$n=1$$

chapter 6 lec 2

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