Question 1

What is the emission of light at only specific wavelengths?
A)Emission spectra
B)Hydrogen spectrum
C)Wave spectra
D)Limited spectra
E)Line spectra

Accepted Answer

Emission of light at only specific wavelengths is known as line spectra. Therefore, the best choice for this question is E) Line spectra.

Question 2

A photon has an energy of 5.53 × 10^-1⁷ J.What is its frequency in s^-1 (h = 6.63 × 10^-34 J • s)? A)3.66 × 10^-50 s^-1 B)1.20 × 10^-1⁷ s^-1 C)3.59 × 10^-9 s^-1 D)2.78 × 10⁸ s^-1 E)8.34 × 10¹⁶ s^-1

Accepted Answer

The frequency of a photon is calculated using the formula $ f = \frac{E}{h} $. Substituting the given values, $ f = \frac{5.53 \times 10^{-17} \text{ J}}{6.63 \times 10^{-34} \text{ J s}} = 8.34 \times 10^{16} \text{ s}^{-1} $.

Question 3

The size of an atomic orbital is associated with
A)the principal quantum number (n).
B)the angular momentum quantum number (l).
C)the magnetic quantum number (ml).
D)the spin quantum number (ms).
E)the angular momentum and magnetic quantum numbers,together.

Accepted Answer

The size of an atomic orbital is associated with the principal quantum number (n), which determines the distance from the nucleus that the electron can occupy. As n increases, the size of the orbital also increases.

Question 4

Line spectra from all regions of the electromagnetic spectrum,including the Paschen series of infrared lines for hydrogen,are used by astronomers to identify elements present in the atmospheres of stars.Calculate the wavelength of the photon emitted when the hydrogen atom undergoes a transition from n = 5 to n = 3.(R = 1.096776 × 10⁷ m^-1) A)205.1 nm B)384.6 nm C)683.8 nm D)1282 nm E)> 1500 nm

Accepted Answer

The answer of Line spectra from all regions of the...

Question 5

Calculate the energy,in joules,required to excite a hydrogen atom by causing an electronic transition from the n = 1 to the n = 4 principal energy level.Recall that the energy levels of the H atom are given by En = -2.18 × 10^-18 J(1/n2 ). A)2.07 × 10^-29 J B)2.19 × 10⁵ J C)2.04 × 10^-1⁸ J D)3.27 × 10^-1⁷ J E)2.25 × 10^-1⁸ J

Accepted Answer

The answer of Calculate the energy,in joules,required to excite a...

Question 6

Calculate the frequency of the light emitted by a hydrogen atom during a transition of its electron from the n = 4 to the n = 1 principal energy level.Recall that for hydrogen En = -2.18 × 10^-1⁸ J(1/n² ).(h = 6.63 × 10^-34 J • s) A)3.08 × 10¹⁵ s^-1 B)1.03 × 10⁸ s^-1 C)2.06 × 10¹⁴ ^s-1 D)1.35 × 10^-51 ^s-1 E)8.22 × 10¹⁴ ^s-1

Accepted Answer

The correct answer is A.The frequency of the light emitted by a hydrogen atom during a transition of its electron from the n = 4 to the n = 1 principal energy level can be calculated using the formula:$$f = \frac{\Delta E}{h}$$where:* f is the frequency of the light emitted* ΔE is the energy difference between the two energy levels* h is Planck's constantThe energy difference between the two energy levels can be calculated using the formula:$$\Delta E = E_f - E_i$$where:* Ef is the energy of the final energy level* Ei is the energy of the initial energy levelThe energy of a hydrogen atom in a particular energy level is given by the formula:$$E_n = -\frac{2.18 	imes 10^{-18} J}{n^2}$$where:* En is the energy of the atom in the nth energy level* n is the principal energy levelSubstituting the values of Ef and Ei into the formula for ΔE, we get:$$\Delta E = -\frac{2.18 	imes 10^{-18} J}{1^2} - \left(-\frac{2.18 	imes 10^{-18} J}{4^2}ight)$$$$\Delta E = -2.18 	imes 10^{-18} J + \frac{2.18 	imes 10^{-18} J}{16}$$$$\Delta E = -2.18 	imes 10^{-18} J + 0.13625 	imes 10^{-18} J$$$$\Delta E = -2.04375 	imes 10^{-18} J$$Substituting the values of ΔE and h into the formula for f, we get:$$f = \frac{-2.04375 	imes 10^{-18} J}{6.63 	imes 10^{-34} J \cdot s}$$$$f = 3.08 	imes 10^{15} s^{-1}$$Therefore, the frequency of the light emitted by a hydrogen atom during a transition of its electron from the n = 4 to the n = 1 principal energy level is 3.08 × 10^15 s^-1.

Question 7

The de Broglie equation predicts that the wavelength (in m)of a proton moving at 1000.m/s is ________________.(h = 6.63 × 10^-34 J • s; mass of a proton = 1.673 × 10^-24 g) A)3.96 × 10^-1⁰ m B)3.96 × 10^-7 m C)2.52 × 10⁶ m D)2.52 × 10⁹ m E)> 10¹⁰ m

Accepted Answer

The de Broglie wavelength is calculated using λ = h / (mv). Converting the mass of the proton to kg (1.673 × 10^-27 kg) and using the given velocity, λ = 6.63 × 10^-34 / (1.673 × 10^-27 * 1000) = 3.96 × 10^-10 m.

Question 8

Calculate the wavelength of a neutron that has a velocity of 200.cm/s.(mass of a neutron = 1.675 × 10^-27 kg and h = 6.63 × 10^-34 J • s) A)1.98 × 10^-9 m B)216 nm C)1.8 × 10⁵⁰ m D)198 nm E)5.05 mm

Accepted Answer

The de Broglie wavelength is calculated using λ = h / (mv). Substituting the given values, λ = 6.63 × 10^-34 J·s / (1.675 × 10^-27 kg × 2 m/s) = 1.98 × 10^-9 m, which is equivalent to 198 nm.

Question 9

Atomic orbitals developed using quantum mechanics
A)describe regions of space in which one is most likely to find an electron.
B)describe exact paths for electron motion.
C)give a description of the atomic structure which is essentially the same as the Bohr model.
D)allow scientists to calculate an exact volume for the hydrogen atom.
E)are in conflict with the Heisenberg uncertainty principle.

Accepted Answer

Atomic orbitals developed using quantum mechanics describe regions of space in which one is most likely to find an electron. However, they do not describe exact paths for electron motion.

Answer: B)
 Atomic orbitals developed using quantum mechanics do not describe exact paths for electron motion. Instead, they describe the probability of finding an electron in a certain region of space.

Answer: C)
 The atomic structure described by atomic orbitals developed using quantum mechanics is fundamentally different from the Bohr model. The Bohr model describes electrons as orbiting the nucleus in fixed, circular orbits, while atomic orbitals describe electrons as existing in probability distributions around the nucleus.

Answer: D)
 Atomic orbitals developed using quantum mechanics do not allow scientists to calculate an exact volume for the hydrogen atom, as they describe electron probability distributions rather than fixed orbits.

Answer: E)
 Atomic orbitals developed using quantum mechanics are not in conflict with the Heisenberg uncertainty principle. In fact, they arise from the application of the uncertainty principle to the behavior of electrons in atoms.

Question 10

Which scientist proposed that energy of radiation is composed of extremely small indivisible packages called quanta? ("Quanta" is the plural of "quantum.")
A)Max Planck
B)Louis de Broglie
C)Clinton Davisson
D)Sir Isaac Newton
E)Lothan Meyer

Accepted Answer

Max Planck proposed the concept of quanta in 1900, which revolutionized the understanding of energy and radiation.

Question 11

If the energy of a photon is 1.32 × 10^-1⁸ J,what is its wavelength in nm (c = 3.00 × 10⁸ m/s; h = 6.63 × 10^-34 J • s)? A)1.51 × 10^-7 nm B)151 nm C)1.99 × 10¹⁵ nm D)1.99 × 10²⁴ nm E)None of these choices is correct.

Accepted Answer

The wavelength λ can be calculated using the formula λ = hc/E. Substituting the given values, λ = (6.63 × 10^-34 J·s * 3.00 × 10^8 m/s) / (1.32 × 10^-18 J) = 1.51 × 10^-7 m = 151 nm.

Question 12

Calculate the wavelength,in nanometers,of the light emitted by a hydrogen atom when its electron falls from the n = 7 to the n = 4 principal energy level.Recall that the energy levels of the H atom are given by En = -2.18 × 10^-1⁸ J (1/n²).(c = 3.00 × 10⁸ m/s; h = 6.63 × 10^-34 J • s) A)4.45 × 10^-20 nm B)2.16 × 10^-6 nm C)9.18 × 10^-20 nm D)1.38 × 10¹⁴ nm E)2.17 × 10³ nm

Accepted Answer

The energy difference between the levels is calculated using En = -2.18 × 10^-18 J (1/n^2). The energy difference is converted to wavelength using E = hc/λ. The correct wavelength is approximately 2.17 × 10^3 nm.

Question 13

The energy of an electron in the hydrogen atom is determined by
A)the principal quantum number (n)only.
B)the angular momentum quantum number (l)only.
C)the principal and angular momentum quantum numbers (n & l).
D)the principal and magnetic quantum numbers (n & ml).
E)the principal,angular momentum,and magnetic quantum numbers.

Accepted Answer

The energy of an electron in a hydrogen atom is determined by the principal quantum number (n) only, as it defines the energy level or shell of the electron.

Question 14

A sprinter must average 24.0 mi/h to win a 100-m dash in 9.30 s.What is his wavelength at this speed if his mass is 84.5 kg ? (h = 6.63 × 10^-34 J • s) A)7.31 × 10^-37 m B)3.26 × 10^-37 m C)5.08 × 10^-30 m D)1.34 × 10^-30 m E)None of these choices is correct.

Accepted Answer

The de Broglie wavelength is given by:$$\lambda = \frac{h}{p} = \frac{h}{mv}$$where:* $$\lambda$$ is the wavelength* $$h$$ is the Planck constant* $$p$$ is the momentum* $$m$$ is the mass* $$v$$ is the velocityWe are given:* $$m = 84.5 	ext{ kg}$$* $$v = 24.0 	ext{ mi/h} = 10.7 	ext{ m/s}$$* $$h = 6.63 	imes 10^{-34} 	ext{ J} \cdot 	ext{s}$$First, we need to convert the velocity to m/s:$$v = 24.0 	ext{ mi/h} = 10.7 	ext{ m/s}$$Now, we can plug in the values:$$\lambda = \frac{h}{mv} = \frac{6.63 	imes 10^{-34} 	ext{ J} \cdot 	ext{s}}{(84.5 	ext{ kg})(10.7 	ext{ m/s})} = 7.31 	imes 10^{-37} 	ext{ m}$$Therefore, the correct answer is A.

Question 15

The word _________ is used as an acronym for the amplification of light which is stimulated by the emission of radiation.
A)beam
B)laser
C)emit
D)brighten
E)light

Accepted Answer

The acronym for the amplification of light which is stimulated by the emission of radiation is laser.

Question 16

The shape of an atomic orbital is associated with
A)the principal quantum number (n).
B)the angular momentum quantum number (l).
C)the magnetic quantum number (ml).
D)the spin quantum number (ms).
E)the magnetic and spin quantum numbers,together.

Accepted Answer

The shape of an atomic orbital is associated with the angular momentum quantum number (l). The value of l determines the kind of orbital: l = 0 corresponds to an s orbital, l = 1 corresponds to a p orbital, l = 2 corresponds to a d orbital, and so on. The value of l also determines the shape of the orbital. For example, an s orbital is spherically symmetric and has no nodal surfaces, while a p orbital has a dumbbell shape and has one nodal surface.

Question 17

According to the Heisenberg uncertainty principle,if the uncertainty in the speed of an electron is 3.5 × 10³ m/s,the uncertainty in its position (in m)is at least ___________.(mass of an electron = 9.11 × 10^-28 g) A)1.7 × 10^-8 m B)6.6 × 10^-8 m C)17 m D)66 m E)None of these choices is correct.

Accepted Answer

The answer of According to the Heisenberg uncertainty principle,if the...

Question 18

Calculate the wavelength associated with a ²⁰Ne⁺ ion moving at a velocity of 2.0 × 10⁵ m/s.The atomic mass of Ne-20 is 19.992 amu.(1 amu = 1.66 × 10^-24 g and h = 6.63 × 10^-34 J • s) A)1.0 × 10^-1³ m B)1.0 × 10^-1⁶ m C)1.0 × 10^-1⁸ m D)9.7 × 10¹² m E)2.0 × 10^-1³ cm

Accepted Answer

The de Broglie wavelength is given by:λ = h/pwhere:λ is the wavelengthh is Planck's constantp is the momentumThe momentum of the ion is:p = mvwhere:m is the mass of the ionv is the velocity of the ionThe mass of the ion is:m = 19.992 amu * 1.66 × 10^-24 g/amu = 3.31 × 10^-23 gThe velocity of the ion is:v = 2.0 × 10^5 m/sThe momentum of the ion is:p = (3.31 × 10^-23 g) * (2.0 × 10^5 m/s) = 6.62 × 10^-18 kg m/sThe wavelength of the ion is:λ = h/p = (6.63 × 10^-34 J • s) / (6.62 × 10^-18 kg m/s) = 1.0 × 10^-13 mTherefore, the correct answer is A.

Question 19

The orientation in space of an atomic orbital is associated with
A)the principal quantum number (n).
B)the angular momentum quantum number (l).
C)the magnetic quantum number (ml).
D)the spin quantum number (ms).
E)none of these choices is correct.

Accepted Answer

The magnetic quantum number (ml) determines the orientation of an atomic orbital in space.

Question 20

Use the Rydberg equation to calculate the frequency of a photon absorbed when the hydrogen atom undergoes a transition from n₁ = 2 to n₂ = 4.(R = 1.096776 × 10⁷ m^-1; c = 3.00 × 10⁸ m/s) A)2.06 × 10⁶ s^-1 B)2.74 × 10⁶ s^-1 C)6.17 × 10¹⁴ s^-1 D)8.23 × 10¹⁴ s^-1 E)> 10¹⁵ s^-1

Accepted Answer

The answer of Use the Rydberg equation to calculate the...

Quiz 6: Quantum Theory and the Electronic Structure of Atoms

What is the emission of light at only specific wavelengths?

A photon has an energy of 5.53 × 10^-1⁷ J.What is its frequency in s^-1 (h = 6.63 × 10^-34 J • s) ?

The size of an atomic orbital is associated with

Calculate the energy,in joules,required to excite a hydrogen atom by causing an electronic transition from the n = 1 to the n = 4 principal energy level.Recall that the energy levels of the H atom are given by En = -2.18 × 10^-18 J(1/n2 ) .

Calculate the frequency of the light emitted by a hydrogen atom during a transition of its electron from the n = 4 to the n = 1 principal energy level.Recall that for hydrogen En = -2.18 × 10^-1⁸ J(1/n² ) .(h = 6.63 × 10^-34 J • s)

The de Broglie equation predicts that the wavelength (in m) of a proton moving at 1000.m/s is ________________.(h = 6.63 × 10^-34 J • s; mass of a proton = 1.673 × 10^-24 g)

Calculate the wavelength of a neutron that has a velocity of 200.cm/s.(mass of a neutron = 1.675 × 10^-27 kg and h = 6.63 × 10^-34 J • s)

Atomic orbitals developed using quantum mechanics

Which scientist proposed that energy of radiation is composed of extremely small indivisible packages called quanta? ("Quanta" is the plural of "quantum.")

If the energy of a photon is 1.32 × 10^-1⁸ J,what is its wavelength in nm (c = 3.00 × 10⁸ m/s; h = 6.63 × 10^-34 J • s) ?

Calculate the wavelength,in nanometers,of the light emitted by a hydrogen atom when its electron falls from the n = 7 to the n = 4 principal energy level.Recall that the energy levels of the H atom are given by En = -2.18 × 10^-1⁸ J (1/n²) .(c = 3.00 × 10⁸ m/s; h = 6.63 × 10^-34 J • s)

The energy of an electron in the hydrogen atom is determined by

A sprinter must average 24.0 mi/h to win a 100-m dash in 9.30 s.What is his wavelength at this speed if his mass is 84.5 kg ? (h = 6.63 × 10^-34 J • s)

The word _________ is used as an acronym for the amplification of light which is stimulated by the emission of radiation.

The shape of an atomic orbital is associated with

According to the Heisenberg uncertainty principle,if the uncertainty in the speed of an electron is 3.5 × 10³ m/s,the uncertainty in its position (in m) is at least ___________.(mass of an electron = 9.11 × 10^-28 g)

Calculate the wavelength associated with a ²⁰Ne⁺ ion moving at a velocity of 2.0 × 10⁵ m/s.The atomic mass of Ne-20 is 19.992 amu.(1 amu = 1.66 × 10^-24 g and h = 6.63 × 10^-34 J • s)

The orientation in space of an atomic orbital is associated with

Use the Rydberg equation to calculate the frequency of a photon absorbed when the hydrogen atom undergoes a transition from n₁ = 2 to n₂ = 4.(R = 1.096776 × 10⁷ m^-1; c = 3.00 × 10⁸ m/s)

Quiz 6: Quantum Theory and the Electronic Structure of Atoms

What is the emission of light at only specific wavelengths?

A photon has an energy of 5.53 × 10-17 J.What is its frequency in s-1 (h = 6.63 × 10-34 J • s) ?

The size of an atomic orbital is associated with

Calculate the energy,in joules,required to excite a hydrogen atom by causing an electronic transition from the n = 1 to the n = 4 principal energy level.Recall that the energy levels of the H atom are given by En = -2.18 × 10-18 J(1/n2 ) .

Calculate the frequency of the light emitted by a hydrogen atom during a transition of its electron from the n = 4 to the n = 1 principal energy level.Recall that for hydrogen En = -2.18 × 10-18 J(1/n2 ) .(h = 6.63 × 10-34 J • s)

The de Broglie equation predicts that the wavelength (in m) of a proton moving at 1000.m/s is ________________.(h = 6.63 × 10-34 J • s; mass of a proton = 1.673 × 10-24 g)

Calculate the wavelength of a neutron that has a velocity of 200.cm/s.(mass of a neutron = 1.675 × 10-27 kg and h = 6.63 × 10-34 J • s)