chpt 3 quantum mechanics and electron configuration

How many electrons in an atom can have the following quantum numbers? n = 4, ℓ = 2, mℓ = -2, ms = +½

1

What is the energy of light that must be absorbed by a hydrogen atom to transition an electron from n = 3 to n = 6?

1.82 × 10⁻¹⁹ J, .The Bohr model of the atom states that the energy required to transition between two energy levels is equal to the difference between the inverse squares of the energy levels multiplied by the Rydberg constant:

How many electrons in an atom can have the following quantum numbers? n = 3, ℓ = 2

10, The maximum number of possible electrons in an atom is dictated by the quantum number ℓ, which in this case equals 2. The value for the quantum number mℓ must be between -ℓ and ℓ, which means mℓ can equal -2, -1, 0, 1, 2. Because each of these values of mℓ has corresponding values n = 3 and ℓ = 2, this represents 5 unique orbitals. The fourth quantum number, ms, can equal +1/2 or -1/2, meaning each orbital can contain two electrons with unique sets of four quantum numbers. Since there are 5 orbitals with the capacity for 2 electrons each, there can be 10 electrons in the atom with n = 3 and ℓ = 2.

Platinum has a work function (Φ) of 6.35 eV. What is the longest wavelength of light, in nm, that will cause the ejection of electrons? (1 eV=1.6 × 10⁻¹⁹ J)

195 nm, The minimum energy required to remove an electron leaves the ejected electron with zero kinetic energy, so the energy will equal the work function. Since the energy (E) of a photon of light is inversely proportional to its wavelength (λ), the minimum energy is equal to the maximum wavelength. After converting the work function from eV to J, this equation can be solved for the maximum wavelength:

In Einstein's photoelectric experiment, the kinetic energy (K.E.) of an electron displaced from a metal by a photon was the difference between the energy of a photon and a threshold energy value for the metal. If you were to perform a similar experiment with lead, which has a threshold energy of 6.81 × 10⁻¹⁹ J, and ultraviolet light of wavelength 38.5 nm, what would be the speed (v) of the dislodged electron in meters per second? (K.E. = 1/2mv². The mass of the electron = 9.109 × 10⁻³¹ kg.)

3.14 × 10⁶ m/s, First calculate the energy of a photon of light with a wavelength of 38.5 nm (which is 38.5×10−938.5×10−9 meters). The kinetic energy of the electron will be the difference between the energy of the photon and the threshold energy of the metal. Calculate the speed from the kinetic energy. Remember that 1 joule = (1 kg⋅m2s21 kg⋅m2)/s2

Arsenic is a toxic solid often used in the past as a component of pesticides. How many electrons are present in a neutral atom of arsenic?

33

A photon of blue light has a frequency of 7.5 × 10¹⁴ Hz. Calculate the wavelength of this photon (c = 3.00 × 10⁸ m/s) in nanometers.

400 nm, .The wavelength (λ) of a photon is equal to the speed of light (c) divided by the frequency (ν):

Scientists are studying ways to improve the efficiency of solar cells by studying a process called photon upconversion. In this process, the energy of two photons can become combined to form a new photon with an energy equal to the sum of the two combined photons. With this process, abundant infrared radiation can be converted into visible light that can be used by solar cells to produce electricity. Suppose an infrared photon with a wavelength of 853 nm were combined with another infrared photon with a wavelength of 915 nm, what would be the wavelength of the new 'combined' photon, in nm?

441 nm, .Calculate the energy of each photon, add the energies to get the energy of the new photon, then calculate the wavelength of the new photon.

Arsenic is a toxic solid often used in the past as a component of pesticides. Counting only s & p electrons, how many valence electrons are present in a neutral atom of arsenic?

5

What is the frequency of green light that has a wavelength of 531 nm? (c = 3.00 x 10⁸ m/s)

5.65 × 10¹⁴ s⁻¹, Given the wavelength of electromagnetic radiation, the frequency can be determined by converting the wavelength into units of meters and then rearranging the equation.

Arsenic is a toxic solid often used in the past as a component of pesticides. Which of the following represents the correct ground-state configuration for a neutral atom of arsenic? A) 1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p³ B) 1s²2s²2p⁶3s²3p⁶4s²4p³ C) 1s²2s²2p⁶3s²3p⁶4s²3d¹⁰ D) 1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p⁶

A) 1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p³

Which of the following atoms is paramagnetic? A) Al B) Ba C) Kr D) Zn E) Xe

A) Al

Which of the following electron configurations is incorrect? A) S [Ne]3s³3p⁴ B) Sn [Kr]5s²4d¹⁰5p² C) Rb [Kr]5s¹ D) V [Ar]4s²3d³ E) I [Kr]5s²4d¹⁰5p⁵

A) S [Ne]3s³3p⁴

True or false: two electrons can simultaneously occupy the same (n,ℓ,mℓ) orbital. A) True B) False

A) True, The fourth quantum number, the spin number (ms), allows for two electrons to have the same n, ℓ, mℓ quantum numbers, but different values for ms.

Which of the following is the electron configuration for Ba? A) [Xe]6s² B) [Rn]6s² C) [Xe]6s¹ D) [Xe]7s² E) [Rn]7s²

A) [Xe]6s²

An electron is shown to occupy a d orbital. Which of the following sets of quantum numbers can describe this electron? A) n = 3, ℓ = 2, mℓ = -2 B) n = 4, ℓ = 1, mℓ = 2 C) n = 5, ℓ = 1, mℓ = 0 D) n = 3, ℓ = 1, mℓ = -1 E) n = 4, ℓ = 3, mℓ = -3

A) n = 3, ℓ = 2, mℓ = -2

The ground state electron configuration of an Al atom is A)1s²2s²2p⁶3s²3d¹ B) 1s²2s²2p⁶3s²3p¹ C) 1s²2s²2p⁶3s²3p⁶4s²4p¹ D) 1s²2s²2p⁶3s²3p² E)1s²2s²2p¹

B) 1s²2s²2p⁶3s²3p¹

Which element has the ground state electron configuration [Ar]4s²3d¹⁰4p⁵? A) As B) Br C) Se D) Te E) I

B) Br

Which element has the electron configuration 1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p²? A) Si B) Ge C) Sn D) Ga E) As

B) Ge

Which quantum state (n,ℓ,mℓ) is NOT possible? A) (2,0,0) B) (3,1,-1) C) (3,0,1) D) (3,2,2) E) (16,15,14)

C) (3,0,1), The value of mℓ must be in the range of -ℓ to +ℓ. Since ℓ = 0, the only possible value for mℓ is 0.

The ground state electron configuration of a Se atom is A) 1s²2s²2p⁶3s²3p⁶4s²4p⁴ B) 1s²2s²2p⁶3s²3p⁶4s²4d¹⁰4p⁴ C) 1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p⁴ D) 1s²2s²2p⁶3s²3p⁴ E) 1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p³

C) 1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p⁴

For which atomic orbital does n = 3 and ℓ = 1? A) 2s B) 3s C) 3p D) 3d E) 4d

C) 3p

Which of the following atoms is diamagnetic? A) Mn B) O C) Sr D) Li E) Cl

C) Sr

Which particle would have the longest de Broglie wavelength traveling with the same velocity? A) He B) Xe C) electron D) neutron E) Not enough info

C) electron, For different particles moving at the same speed, the particle with the smallest mass will have the longest wavelength. Because the electron is the lightest of the options given, it will have the longest de Broglie wavelength.

Which of the following sets of quantum numbers is not allowed? A) n = 2, ℓ = 0, mℓ = 0 B) n = 3, ℓ = 2, mℓ = 0 C) n = 2, ℓ = 2, mℓ = 2 D) n = 3, ℓ = 1, mℓ = -1 E) n = 4, ℓ = 2, mℓ = 1

C) n = 2, ℓ = 2, mℓ = 2

Which of the following sets of quantum numbers can describe a 3p electron? A) n = 1, ℓ = 3, mℓ = 1 B) n = 3, ℓ = 2, mℓ = 1 C) n = 3, ℓ = 1, mℓ = 1 D) n = 3 , ℓ = 0, mℓ = 1 E) n = 2, ℓ = 3, mℓ = 1

C) n = 3, ℓ = 1, mℓ = 1

Arsenic is a toxic solid often used in the past as a component of pesticides. Which of the following represents the correct ground-state configuration for the arsenide ion? A) 1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p³ B) 1s²2s²2p⁶3s²3p⁶4s²4p³ C) 1s²2s²2p⁶3s²3p⁶4s²3d¹⁰ D) 1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p⁶

D) 1s²2s²2p⁶3s²3p⁶4s²3d¹⁰4p⁶

The electron configuration of Fe²⁺ is [Ar]3d⁶. Which of the following is true about Fe²⁺? A) Fe²⁺ is diamagnetic. B) Fe²⁺ is paramagnetic with one unpaired electron C) Fe²⁺ is paramagnetic with two unpaired electrons D) Fe²⁺ is paramagnetic with four unpaired electrons. E) Fe²⁺ is paramagnetic with five unpaired electrons.

D) Fe²⁺ is paramagnetic with four unpaired electrons.

Which element has the electron configuration 1s²2s²2p⁶3s²3p⁶4s²3d⁵? A) Fe B) Tc C) Cr D) Mn E) Mo

D) Mn

Energy of a photon is ______ proportional to frequency, and _______ proportional to wavelength. A) directly, directly B) inversely, inversely C) directly, not D) directly, inversely E) inversely, directly

D) directly, inversely, E=hν=hc/λ

Which color (frequency) of light travels the fastest in a vacuum? A) Red B) Yellow C) Green D) Violet E) All have the same speed

E) All have the same speed, All light travels at the same speed (c) regardless of wavelength or frequency.