Question 1

Determine the wavelength of the line in the hydrogen atom spectrum corresponding to the n₁ F1F1F1S1F1F1F10 3 to n₂ F1F1F1S1F1F1F10 4 transition. A)1,094 nm B)1,875 nm C)656 nm D)335 nm E)109 nm

Accepted Answer

The transition from n=4 to n=3 in the hydrogen atom corresponds to the Paschen series, which is in the infrared region. The wavelength for this transition is approximately 1,875 nm.

Question 2

How much energy is required to ionize one mole of HeF1F1F1S1^F1F1F10 ions in their ground state? A)5,251 kJ B)2,178 kJ C)3,764 kJ D)1,234 kJ E)757 kJ

Accepted Answer

The correct answer is A because the energy required to ionize one mole of HeF1F1F1S1^F1F1F10 ions in their ground state is 5,251 kJ.

Question 3

What is the speed of an argon atom that has a de Broglie wavelength of 5.2 pm? A)0.52 m/s B)5.2 F1F1F1S1F1F1F10 10³ m/s C)1.9 F1F1F1S1F1F1F10 10³ m/s D)1.9 m/s E)25 m/s

Accepted Answer

The de Broglie wavelength of a particle is given by λ = h/mv, where h is Planck's constant, m is the mass of the particle, and v is its velocity. Rearranging the equation, we get v = h/(mλ). 
Substituting the given values, we get v = (6.626 x 10^-34 J.s)/[(39.948 g/mol)/(6.022 x 10^23/mol) x 5.2 x10^-12 m] 
Simplifying, we get v = 1.89 x 10^3 m/s, which is closest to choice C: 1.9 x 10^3 m/s.

Question 4

Early photoelectric light detectors were based on cesium. Cesium metal has a work function of 3.43  F1F1F1S1F1F1F10J. What is the longest wavelength of light that could be detected with one of these detectors?
A)759 nm
B)579 nm
C)679 nm
D)767 nm
E)455 nm

Accepted Answer

The answer of Early photoelectric light detectors were based on...

Question 5

How much energy is required to ionize an HeF1F1F1S1^F1F1F10 ion in its ground state? A)2.18 F1F1F1S1F1F1F10J B)4.36 F1F1F1S1F1F1F10J C)8.72 F1F1F1S1F1F1F10J D)1.74 F1F1F1S1F1F1F10J

Accepted Answer

The answer of How much energy is required to ionize...

Question 6

Which transition in a hydrogen atom will cause emission of the shortest wavelength photon? A)n₁ F1F1F1S1F1F1F104 to n₂ F1F1F1S1F1F1F103 B)n₁ F1F1F1S1F1F1F104 to n₂ F1F1F1S1F1F1F102 C)n₁ F1F1F1S1F1F1F103 to n₂ F1F1F1S1F1F1F102 D)n₁ F1F1F1S1F1F1F103 to n₂ F1F1F1S1F1F1F101 E)n₁ F1F1F1S1F1F1F1010 to n₂ F1F1F1S1F1F1F109

Accepted Answer

The answer of Which transition in a hydrogen atom will...

Question 7

Which of the transitions in the hydrogen atom energy-level diagram shown here is not possible? 
A)a
B)b
C)c
D)d

Accepted Answer

Transition d is not possible because it violates the energy conservation principle. The energy difference between levels n=2 and n=1 is 10.2 eV, and the energy difference between levels n=1 and n=3 is 12.1 eV. Therefore, to move from level n=2 to level n=3, the atom would need to absorb a photon with exactly 1.9 eV of energy, which is not possible since no such photon exists in the electromagnetic spectrum.

Question 8

Which of the transitions in the hydrogen atom energy-level diagram shown here requires the longest wavelength photon? 
A)a
B)b 
C)c
D)d

Accepted Answer

The transition from level 3 to level 2 (C) requires the longest wavelength photon because it has the lowest energy difference between the levels. This means that the photon must have a lower frequency and longer wavelength to supply the energy needed for the transition.

Question 9

How much energy is required to ionize one mole of hydrogen atoms in their ground state?
A)1,312 kJ
B)2.18 kJ
C)218 kJ
D)2,178 kJ
E)131.2 kJ

Accepted Answer

The energy required to ionize one mole of hydrogen atoms in their ground state is 1,312 kJ. This is because the ionization energy for a single hydrogen atom is 13.6 eV, and when converting this value for one mole of atoms using Avogadro's number and the conversion factor between electron volts and joules, the result is approximately 1,312 kJ.

Question 10

The change in energy of a one-electron atom or ion for an electronic transition from the initial energy level n_i to the final energy level n_f is given by Which of the following species will have the longest wavelength emission line for the transition between the n_i F1F1F1S1F1F1F10 2 and n_f F1F1F1S1F1F1F10 1 levels? A)H B)HeF1F1F1S1^F1F1F10 C)Li²F1F1F1S1^F1F1F10 D)Be³F1F1F1S1^F1F1F10 E)B⁴F1F1F1S1^F1F1F10

Accepted Answer

The energy change for the transition is given by the formula 11eaa952_9bcd_f584_ae90_75cfb6f82ff7_TB3835_11, which depends on the initial and final energy levels only. Therefore, the wavelength of the emitted radiation, which is inversely proportional to the energy change, will be the same for all species undergoing this transition. However, the energy levels of the hydrogen atom are uniquely given by En = -13.6/n^2 eV, where n is an integer, and the transition from n=2 to n=1 gives the famous "Lyman alpha" emission at 121.6 nm, which is the longest wavelength (lowest energy) line in the Lyman series. Therefore, the correct answer is A.

Question 11

Recently, buckyballs (C₆₀) became the largest objects with a measured de Broglie wavelength. If the mass of a C₆₀ molecule is 1.20 F1F1F1S1F1F1F10kg, what will be its de Broglie wavelength if it is moving at a speed of 220 m/sec? A)2.52 pm B)2.52 fm C)2.52 m D)1.20 pm E)5.22 m

Accepted Answer

The answer of Recently, buckyballs (C₆₀) became the largest objects...

Question 12

Which transition in a hydrogen atom requires the smallest change in energy? A)n₁ F1F1F1S1F1F1F101 to n₂ F1F1F1S1F1F1F102 B)n₁ F1F1F1S1F1F1F103 to n₂ F1F1F1S1F1F1F104 C)n₁ F1F1F1S1F1F1F102 to n₂ F1F1F1S1F1F1F103 D)n₁ F1F1F1S1F1F1F103 to n₂ F1F1F1S1F1F1F105 E)n₁ F1F1F1S1F1F1F104 to n₂ F1F1F1S1F1F1F105

Accepted Answer

The answer of Which transition in a hydrogen atom requires...

Question 13

Which of the transitions in the following hydrogen atom energy-level diagram involves the shortest wavelength photon? 
A)a
B)b
C)c
D)d

Accepted Answer

The answer of Which of the transitions in the following...

Question 14

Which of the following electrons will have the smallest de Broglie wavelength?
A)an electron moving 220 m/sec
B)an electron moving 20 mi/hr
C)an electron moving 75 km/hr
D)an electron moving at 25% the speed of light
E)an electron at rest with no velocity

Accepted Answer

The de Broglie wavelength ($\lambda$) is given by the equation $\lambda = \frac{h}{mv}$, where $h$ is Planck's constant, $m$ is the mass of the particle, and $v$ is the velocity of the particle. The smaller the wavelength, the higher the velocity of the particle. An electron moving at 25% the speed of light (option D) would have the highest velocity among the options provided, thus the smallest de Broglie wavelength.

Question 15

What wavelength of light is required to cause the ejection of photoelectrons with kinetic energies of 5.0  F1F1F1S1F1F1F10J from a calcium surface (F1F1F1S1F1F1F10 F1F1F1S1F1F1F10 4.60  F1F1F1S1F1F1F10J)?
A)485 nm
B)390 nm
C)308 nm
D)632 nm
E)480 nm

Accepted Answer

The answer of What wavelength of light is required to...

Question 16

Determine the wavelength of the line in the hydrogen atom spectrum corresponding to the n₁ F1F1F1S1F1F1F10 2 to n₂ F1F1F1S1F1F1F10 6 transition. A)1,275 nm B)1,034 nm C)595 nm D)410 nm E)225 nm

Accepted Answer

The wavelength of the line in the hydrogen atom spectrum for a transition can be calculated using the Rydberg formula: $ \frac{1}{\lambda} = R \left( \frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}} \right) $, where $ \lambda $ is the wavelength, $ R $ is the Rydberg constant ($ 1.097 \times 10^{7} \, m^{-1} $), $ n_{1} $ is the lower energy level, and $ n_{2} $ is the higher energy level. For the transition from $ n = 2 $ to $ n = 6 $, plugging in the values gives $ \frac{1}{\lambda} = 1.097 \times 10^{7} \left( \frac{1}{2^{2}} - \frac{1}{6^{2}} \right) $, which calculates to a wavelength $ \lambda $ close to 410 nm.

Question 17

Which of the following objects, all moving at the same speed, will have the largest de Broglie wavelength?
A)a proton
B)an electron
C)a bowling ball
D)a neon atom
E)a neutron

Accepted Answer

The de Broglie wavelength is inversely proportional to the mass of the object, so the smaller the mass, the larger the wavelength. Electrons have a much smaller mass than protons, bowling balls, and neon atoms, and neutrons have a similar mass to protons. Therefore, the electron will have the largest de Broglie wavelength among the given options.

Question 18

The energy of a one-electron atom is given by where Z is the atomic number of the element. Which of the following one-electron ions has the largest ionization energy? A)Li²F1F1F1S1^F1F1F10 B)Be³F1F1F1S1^F1F1F10 C)HeF1F1F1S1^F1F1F10 D)B⁴F1F1F1S1^F1F1F10 E)C⁵F1F1F1S1^F1F1F10

Accepted Answer

The ionization energy is defined as the energy required to remove an electron from an atom or ion. For the given one-electron ions, the ionization energy is simply the energy of the atom (given by the expression in the question) with one less electron.

Therefore, we need to choose the ion with the highest energy expression. We notice that all ions have the same energy expression except for the value of Z (atomic number). Since Z is the highest for the ion in choice E (carbon with Z=6), it has the highest energy and therefore the highest ionization energy.

Question 19

Which transition in a hydrogen atom requires the largest change in energy? A)n₁ F1F1F1S1F1F1F102 to n₂ F1F1F1S1F1F1F10 3 B)n₁ F1F1F1S1F1F1F102 to n₂ F1F1F1S1F1F1F10 4 C)n₁ F1F1F1S1F1F1F101 to n₂ F1F1F1S1F1F1F10 3 D)n₁ F1F1F1S1F1F1F101 to n₂ F1F1F1S1F1F1F102 E)n₁ F1F1F1S1F1F1F109 to n₂ F1F1F1S1F1F1F1010

Accepted Answer

The answer of Which transition in a hydrogen atom requires...

Question 20

Determine the wavelength of the line in the hydrogen atom spectrum corresponding to the n₁ F1F1F1S1F1F1F10 4 to n₂ F1F1F1S1F1F1F10 8 transition. A)1,947 nm B)1,632 nm C)1,058 nm D)725 nm E)421 nm

Accepted Answer

The wavelength of the line in the hydrogen atom spectrum corresponding to the n₁ F1F1F1S1F1F1F10 4 to n₂ F1F1F1S1F1F1F10 8 transition can be calculated using the Rydberg formula:$$\frac{1}{\lambda}=R_H(\frac{1}{n_1^2}-\frac{1}{n_2^2})$$where R_H is the Rydberg constant for hydrogen (1.0973731×10^7 m^-1).Substituting the given values into the formula, we get:$$\frac{1}{\lambda}=1.0973731 imes10^7 m^{-1}(\frac{1}{4^2}-\frac{1}{8^2})$$$$\frac{1}{\lambda}=1.0973731 imes10^7 m^{-1}(\frac{1}{16}-\frac{1}{64})$$$$\frac{1}{\lambda}=1.0973731 imes10^7 m^{-1}(\frac{3}{64})$$$$\frac{1}{\lambda}=5.167548 imes10^6 m^{-1}$$$$\lambda=\frac{1}{5.167548 imes10^6 m^{-1}}=1.936 imes10^{-6} m=1,936 nm$$Therefore, the wavelength of the line in the hydrogen atom spectrum corresponding to the n₁ F1F1F1S1F1F1F10 4 to n₂ F1F1F1S1F1F1F10 8 transition is 1,936 nm, which is closest to choice A) 1,947 nm.

Quiz 7: A Quantum Model of Atoms: Waves and Particles

Determine the wavelength of the line in the hydrogen atom spectrum corresponding to the n₁  3 to n₂  4 transition.

How much energy is required to ionize one mole of He^ ions in their ground state?

What is the speed of an argon atom that has a de Broglie wavelength of 5.2 pm?

Early photoelectric light detectors were based on cesium. Cesium metal has a work function of 3.43 J. What is the longest wavelength of light that could be detected with one of these detectors?

How much energy is required to ionize an He^ ion in its ground state?

Which transition in a hydrogen atom will cause emission of the shortest wavelength photon?

Which of the transitions in the hydrogen atom energy-level diagram shown here is not possible?

Which of the transitions in the hydrogen atom energy-level diagram shown here requires the longest wavelength photon?

How much energy is required to ionize one mole of hydrogen atoms in their ground state?

The change in energy of a one-electron atom or ion for an electronic transition from the initial energy level n_i to the final energy level n_f is given by Which of the following species will have the longest wavelength emission line for the transition between the n_i  2 and n_f  1 levels?

Recently, buckyballs (C₆₀) became the largest objects with a measured de Broglie wavelength. If the mass of a C₆₀ molecule is 1.20 kg, what will be its de Broglie wavelength if it is moving at a speed of 220 m/sec?

Which transition in a hydrogen atom requires the smallest change in energy?

Which of the transitions in the following hydrogen atom energy-level diagram involves the shortest wavelength photon?

Which of the following electrons will have the smallest de Broglie wavelength?

What wavelength of light is required to cause the ejection of photoelectrons with kinetic energies of 5.0 J from a calcium surface (  4.60 J) ?

Determine the wavelength of the line in the hydrogen atom spectrum corresponding to the n₁  2 to n₂  6 transition.

Which of the following objects, all moving at the same speed, will have the largest de Broglie wavelength?

The energy of a one-electron atom is given by where Z is the atomic number of the element. Which of the following one-electron ions has the largest ionization energy?

Which transition in a hydrogen atom requires the largest change in energy?

Determine the wavelength of the line in the hydrogen atom spectrum corresponding to the n₁  4 to n₂  8 transition.