Question 1

Carotene,which is partly responsible for the color of carrots,has 22 $\pi$ electrons in a conjugated system and a length of about 3 nm.The lowest energy transition in carotene is from n = ___ to n = ___.

Accepted Answer

The answer of Carotene,which is partly responsible for the color...

Question 2

Consider a one-dimensional particle in a box of length 2L and one of length 3L.Which of the following is true?

Accepted Answer

The energy levels for a particle in a box are given by the equation E = (n^2 * pi^2 * h^2)/(8mL^2), where n is the quantum number, h is Planck's constant, m is the mass of the particle, and L is the length of the box. Since the energy levels depend on the length of the box, the energy levels for the box of length 3L will be higher than those for the box of length 2L. However, the spacing between energy levels is inversely proportional to the length of the box, so the energy levels n = 1 and n = 2 will be closer together for the box of length 3L, making choice A the correct answer. The zero-point energy is the energy of the lowest possible energy level, which is the ground state. Since the formula for energy levels includes n^2, the ground state (n = 1) for both boxes will have a non-zero energy, so neither box will have a zero-point energy of 0. Therefore, choices D and E are incorrect.

Question 3

Which of the following statements with respect to the photoelectric effect is incorrect?

Accepted Answer

The slope of the plot of kinetic energy of the ejected electrons versus the frequency of the incident radiation is equal to Planck's constant (h), not the value of the work function. The work function is the y-intercept of this plot, representing the minimum energy needed to eject electrons.

Question 4

A node is a point at which the wavefunction becomes zero.

Accepted Answer

The answer of A node is a point at which...

Question 5

The Balmer series of lines for the hydrogen atom are found only in the visible region of the spectrum.

Accepted Answer

The Balmer series primarily falls within the visible spectrum, but it also includes lines in the ultraviolet region.

Question 6

The zero-point energy in 1,3-butadiene is larger than in 1,3,5,7-octatetraene.

Accepted Answer

The zero-point energy is the minimum possible energy that a quantum mechanical physical system may have. In general, the zero-point energy increases as the number of vibrational modes in a molecule increases. In 1,3-butadiene, there are four vibrational modes, while in 1,3,5,7-octatetraene, there are eight. Therefore, the zero-point energy in 1,3-butadiene is larger than in 1,3,5,7-octatetraene.

Question 7

All the orbitals of a given shell of He⁺ are degenerate regardless of the value of the orbital angular momentum.

Accepted Answer

The orbitals of a given shell of an atom are always degenerate regardless of the value of the orbital angular momentum. This is because they share the same principal quantum number (n) and therefore have the same energy level.

Question 8

Which of the following is expected to approximate the value of the wavelength of a 5-g bullet traveling at 1300 miles per hour?

Accepted Answer

The answer of Which of the following is expected to...

Question 9

The four $\pi$ electrons of 1,3-butadiene can be modeled as particles in a box.If the length of 1,3-butadiene (L)is 0.56 nm,calculate the energy of the lowest energy transition.

Accepted Answer

The answer of The four $\pi$ electrons of 1,3-butadiene can...

Question 10

Estimate the minimum uncertainty in the position of an electron of mass 9.109 * 10^-³¹ kg,given that its speed is unknown to within ±3.00 * 10⁵m·s^-¹.

Accepted Answer

The uncertainty in position is given by the Heisenberg Uncertainty Principle as:
∆x * ∆p >= h/4π
where ∆x is the uncertainty in position, ∆p is the uncertainty in momentum, and h is Planck's constant. We can rearrange this equation to solve for ∆x:
∆x >= h/4π∆p
Substituting the given values, we get:
∆x >= (6.626 x 10^-34)/(4π x (9.109 x 10^-31) x (3.00 x 10^15))
∆x >= 193 x 10^-12 m
Converting this to picometers, we get:
∆x >= 193 pm
Therefore, the best choice is C.

Question 11

The square of the amplitude of a wave determines the intensity of the radiation.

Accepted Answer

The intensity of radiation is proportional to the square of the amplitude of a wave.

Question 12

What is the shortest-wavelength line in the emission spectrum of the hydrogen atom?

Accepted Answer

The shortest-wavelength line in the hydrogen atom emission spectrum occurs when an electron transitions from the second energy level to the first energy level (n=2 to n=1). This transition corresponds to the emission of a photon with a wavelength of 91.2 nm. Therefore, the correct choice is D.

Question 13

Calculate the longest-wavelength line in the Balmer series for hydrogen.

Accepted Answer

The longest-wavelength line in the Balmer series for hydrogen corresponds to the transition from the n = 2 to the n = 3 energy level. This transition results in the emission of a photon with a wavelength given by:

1/λ = R(1/32 − 1/22)

where R is the Rydberg constant, equal to 1.097 × 107 m−1.

Solving for λ yields:

λ = 656.3 nm

Therefore, the best choice is B (657 nm), which is the closest answer to the calculated value.

Question 14

The planet Mercury has a maximum intensity of solar radiation of 3700 nm on the sunlit side.What is the temperature of the surface of Mercury on the sunlit side? The empirical value of the constant in Wien's law is 2.9 K·mm.

Accepted Answer

The answer of The planet Mercury has a maximum intensity...

Question 15

Which of the following is Wien's law?

Accepted Answer

Wien's law states that the wavelength at which the intensity of black-body radiation is maximum is inversely proportional to the temperature, which is most closely represented by choice A.

Question 16

If a particle is confined to a one-dimensional box of length 300 pm,for $\varPsi$ ₃ the particle is most likely to be found at

Accepted Answer

For a particle in a one-dimensional box in its ground state, the probability density function is given by:
P(x) = [(2/L)]*sin^2[(n*pi*x)/L]
Where L is the length of the box, n is the quantum number (n=1 for the ground state).
For this problem, L=300 pm, and n=1.
Therefore, P(x) = [(2/300 pm)]*sin^2[(pi*x)/300 pm]
The maximum value of sin^2[(pi*x)/300 pm] is 1, which occurs at x=50,150, and 250 pm. Therefore, the particle is most likely to be found at these positions, as stated in choice B.

Question 17

What is the probability of finding an electron in a small region of a hydrogen 1s orbital at a distance 3a₀ from the nucleus relative to the probability of finding it in the same small region located at the nucleus?

Accepted Answer

The answer of What is the probability of finding an...

Question 18

Which of the following metals has the lowest work function?

Accepted Answer

Rb (Rubidium) has the lowest work function among the options given. Work function is the minimum energy needed to remove an electron from the surface of a metal. In general, alkali metals like Rb have lower work functions due to their single valence electron, which is loosely bound compared to elements in other groups.

Question 19

Which of the following emission lines corresponds to part of the Balmer series of lines in the spectrum of a hydrogen atom? (a)n₂ $\rightarrow$n₁ (b)n₄ $\rightarrow$ n₂ (c)n₄ $\rightarrow$ n₁ (d)n₃ $\rightarrow$ n₂ (e)n₄ $\rightarrow$ n₃

Accepted Answer

The Balmer series involves transitions to n=2 from higher energy levels. Thus, transitions n4 to n2 and n3 to n2 are part of the Balmer series.

Question 20

Comparing the lowest energy transition,$\Delta$E,in1,3-butadiene(A)and 1,3,5,7-octatetraene(B),$\Delta$E_A is greater than $\Delta$E_B.

Accepted Answer

The lowest energy transition in compound A involves moving an electron from the F1 orbital to the S1 orbital, while in compound B it involves moving an electron from the F1 orbital to the S1 orbital and also exciting an electron from the E orbital to the U1 orbital. This extra excitation in compound B requires more energy than the transition in compound A, making F1F1F1S1F1F1F10E_A greater than F1F1F1S1F1F1F10E_B.

Quiz 1: The Quantum World

Carotene,which is partly responsible for the color of carrots,has 22 $\pi$ electrons in a conjugated system and a length of about 3 nm.The lowest energy transition in carotene is from n = _ to n = _.

Consider a one-dimensional particle in a box of length 2L and one of length 3L.Which of the following is true?

Which of the following statements with respect to the photoelectric effect is incorrect?

A node is a point at which the wavefunction becomes zero.

The Balmer series of lines for the hydrogen atom are found only in the visible region of the spectrum.

The zero-point energy in 1,3-butadiene is larger than in 1,3,5,7-octatetraene.

All the orbitals of a given shell of He⁺ are degenerate regardless of the value of the orbital angular momentum.

Which of the following is expected to approximate the value of the wavelength of a 5-g bullet traveling at 1300 miles per hour?

The four $\pi$ electrons of 1,3-butadiene can be modeled as particles in a box.If the length of 1,3-butadiene (L)is 0.56 nm,calculate the energy of the lowest energy transition.

Estimate the minimum uncertainty in the position of an electron of mass 9.109 * 10^-³¹ kg,given that its speed is unknown to within ±3.00 * 10⁵m·s^-¹.

The square of the amplitude of a wave determines the intensity of the radiation.

What is the shortest-wavelength line in the emission spectrum of the hydrogen atom?

Calculate the longest-wavelength line in the Balmer series for hydrogen.

The planet Mercury has a maximum intensity of solar radiation of 3700 nm on the sunlit side.What is the temperature of the surface of Mercury on the sunlit side? The empirical value of the constant in Wien's law is 2.9 K·mm.

Which of the following is Wien's law?

If a particle is confined to a one-dimensional box of length 300 pm,for $\varPsi$ ₃ the particle is most likely to be found at

What is the probability of finding an electron in a small region of a hydrogen 1s orbital at a distance 3a₀ from the nucleus relative to the probability of finding it in the same small region located at the nucleus?

Which of the following metals has the lowest work function?

Which of the following emission lines corresponds to part of the Balmer series of lines in the spectrum of a hydrogen atom? (a) n₂ $\rightarrow$ n₁ (b) n₄ $\rightarrow$ n₂ (c) n₄ $\rightarrow$ n₁ (d) n₃ $\rightarrow$ n₂ (e) n₄ $\rightarrow$ n₃

Comparing the lowest energy transition, $\Delta$ E,in1,3-butadiene(A)and 1,3,5,7-octatetraene(B), $\Delta$ E_A is greater than $\Delta$ E_B.

Quiz 1: The Quantum World

Carotene,which is partly responsible for the color of carrots,has 22 π\piπ electrons in a conjugated system and a length of about 3 nm.The lowest energy transition in carotene is from n = ___ to n = ___.

Consider a one-dimensional particle in a box of length 2L and one of length 3L.Which of the following is true?

Which of the following statements with respect to the photoelectric effect is incorrect?

A node is a point at which the wavefunction becomes zero.

The Balmer series of lines for the hydrogen atom are found only in the visible region of the spectrum.

The zero-point energy in 1,3-butadiene is larger than in 1,3,5,7-octatetraene.

All the orbitals of a given shell of He+ are degenerate regardless of the value of the orbital angular momentum.

Which of the following is expected to approximate the value of the wavelength of a 5-g bullet traveling at 1300 miles per hour?

The four π\piπ electrons of 1,3-butadiene can be modeled as particles in a box.If the length of 1,3-butadiene (L)is 0.56 nm,calculate the energy of the lowest energy transition.

Estimate the minimum uncertainty in the position of an electron of mass 9.109 * 10-31 kg,given that its speed is unknown to within ±3.00 * 105m·s-1.

The square of the amplitude of a wave determines the intensity of the radiation.

What is the shortest-wavelength line in the emission spectrum of the hydrogen atom?

Calculate the longest-wavelength line in the Balmer series for hydrogen.

The planet Mercury has a maximum intensity of solar radiation of 3700 nm on the sunlit side.What is the temperature of the surface of Mercury on the sunlit side? The empirical value of the constant in Wien's law is 2.9 K·mm.

Which of the following is Wien's law?

If a particle is confined to a one-dimensional box of length 300 pm,for Ψ\varPsiΨ 3 the particle is most likely to be found at

What is the probability of finding an electron in a small region of a hydrogen 1s orbital at a distance 3a0 from the nucleus relative to the probability of finding it in the same small region located at the nucleus?

Which of the following metals has the lowest work function?

Which of the following emission lines corresponds to part of the Balmer series of lines in the spectrum of a hydrogen atom? (a) n2 →\rightarrow→ n1 (b) n4 →\rightarrow→ n2 (c) n4 →\rightarrow→ n1 (d) n3 →\rightarrow→ n2 (e) n4 →\rightarrow→ n3

Comparing the lowest energy transition, Δ\DeltaΔ E,in1,3-butadiene(A)and 1,3,5,7-octatetraene(B), Δ\DeltaΔ EA is greater than Δ\DeltaΔ EB.

Carotene,which is partly responsible for the color of carrots,has 22 $\pi$ electrons in a conjugated system and a length of about 3 nm.The lowest energy transition in carotene is from n = _ to n = _.

All the orbitals of a given shell of He⁺ are degenerate regardless of the value of the orbital angular momentum.

The four $\pi$ electrons of 1,3-butadiene can be modeled as particles in a box.If the length of 1,3-butadiene (L)is 0.56 nm,calculate the energy of the lowest energy transition.

Estimate the minimum uncertainty in the position of an electron of mass 9.109 * 10^-³¹ kg,given that its speed is unknown to within ±3.00 * 10⁵m·s^-¹.

If a particle is confined to a one-dimensional box of length 300 pm,for $\varPsi$ ₃ the particle is most likely to be found at

What is the probability of finding an electron in a small region of a hydrogen 1s orbital at a distance 3a₀ from the nucleus relative to the probability of finding it in the same small region located at the nucleus?

Which of the following emission lines corresponds to part of the Balmer series of lines in the spectrum of a hydrogen atom? (a) n₂ $\rightarrow$ n₁ (b) n₄ $\rightarrow$ n₂ (c) n₄ $\rightarrow$ n₁ (d) n₃ $\rightarrow$ n₂ (e) n₄ $\rightarrow$ n₃

Comparing the lowest energy transition, $\Delta$ E,in1,3-butadiene(A)and 1,3,5,7-octatetraene(B), $\Delta$ E_A is greater than $\Delta$ E_B.