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The wave function of a particle is shown in the figure below. What is the probability of finding the particle at x1? Assuming the wave function is symmetric, what is the probability of finding the particle at any position between 0 and x2?

The number of 3d states (the number of distinct sets of quantum numbers) for hydrogen is
(a) 32
(b) 18
(c) 14
(d) 10
(e) 8
(f) 5
(g) 4
(h) 2
(i) none of the above

For a hydrogen atom in the 3 p state. what is the value of the smallest possible angle between the angular momentum vector and the z-axis?
(a) 90°
(b) 45°
(c) 35°
(d) zero
(e) none of the above

Consider the spacing of vibrational energy levels of Pb and Al based on the quantum harmonic oscillator model for the interatomic bound. Pb has a stiffness of ks ∼ 5N/m and an atomic mass of 207 mN (where mN is the mass of a nucleon). For Al, the stiffness is ks ∼ 17N/m, and the atomic mass is 27 mN. Determine the ratio of the energy level spacings, ΔEAl / ΔEPb. Choose one:
1. 0.5
2. 1
3. 6
4. 1.33
5. 2
6. 5.11
7. 3.33
8. 4

Which energy diagram in the figure below is appropriate for each of the following situations?
I. Vibrational states of a diatomic molecule such as O 2
II. Idealized quantized spring - mass oscillator
III. Electronic, vibrational, and rotational states of a diatomic molecule such as O2
IV. Electronic states of a single atom such as hydrogen
1. I-C, II-A, III-B, IV-C
2. I-C, II-B, III-D, IV-A
3. I-A, II-C, III-D, IV-B
4. I-A, II-D, III-A, IV-C
5. I-A, II-B, III-D, IV-C
6. I-B, II-A, III-C, IV-D
7. I-B, II-D, III-C, IV-A
8. I-B, II-C, III-A, IV-D
9. I-D, II-C, III-A, IV-B
10. I-D, II-B, III-A, IV-C

1. Which of the following principles is the periodic table mainly based on? (a) It is based on the uncertainty principle (b) All electrons in an atom must have the same set of quantum numbers. (c) No two electrons in an atom can have the same set of quantum numbers.(d) All electrons in an atom are in orbitals having the same energy (e) Energy is conserved in all interactions.2. Give an example to support your choice in Question 1.

Consider an electron in the state n = 4, l = 3, m = 2, s = 1/2.Part A: In what shell is this electron located?Part B: In what subshell is this electron located?Part C: How many other electrons could occupy the same subshell as this electron?

Consider an electron in the state n = 4, l = 3, m = 2, s = 1/2.Part A: What is the z component of the orbital angular momentum of this electron, Lz?Part B: What is the z component of the spin angular momentum of this electron, Sz?

Which of the following phenomena most clearly demonstrates the particle nature of light?A. diffractionB. polarizationC. the photoelectric effectD. refractionE. interference

The glow emitted by a substance exposed to external radiation is called A. bioluminescence. B. luminescence. C. phosphorescence. D. fluorescence.

The allowed energies of a simple atom are 0.0 eV, 4.0 eV, and 6.0 eV.What wavelength(s) appear(s) in the atom's absorption spectrum?

The allowed energies of a quantum system are 1.0 eV, 2.0 eV, 4.0 eV, and 7.0 eV. What wavelengths appear in the system's emission spectrum (in nanometers)?

The Schrödinger equation for a free particle (no potential energy) is :What is the most general solution of the time-independent Schrödinger equation?a) Asin(kx)b) Asin(kx)+Bcos(kx)c) Ae-kx + Bekx

A proton is confined to a space 1 fm wide (about the size of the atomic nucleus). What is the minimum uncertainty in its velocity?

Is it possible to determine an electron’s velocity accurate to ±1.0m/s while simultaneously finding its position to within ±1.0 μm?

Is it possible to determine a proton’s velocity accurate to ±1.0m/s while simultaneously finding its position to within ±1.0 μm?

Which of the following statements are true according to Heisenberg's uncertainty principle? 1)There is a limit to the accuracy of certain measurements. This limit restricts how well measuring instruments can be constructed. 2)The unavoidable interaction between the thing to be observed and the observing instrument accounts for some of the limits on the accuracy of measurements. 3)The wave-particle duality accounts for some of the limits on accuracy of measurements. 4)There is a limit to the accuracy of certain measurements. This limit is a restriction inherent in nature. 5)The position and momentum of an object cannot both be precisely given at the same time.

What are the possible magnetic quantum numbers (ml) associated with each indicated value of l?1. l = 3; ml = ?a. -3, -2, -1, 0, 1, 2, 3b. -3, 3c. 0, 1, 2, 3d. -3, -2, -1, 1, 2, 32. l = 5; ml = ?a. -5, 5b. -5, -4, -3, -2, -1, 1, 2, 3, 4, 5c. 0, 1, 2, 3, 4, 5d. -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5

What wavelengths (nm) appear in the system's emission spectrum?The allowed energies of a quantum system are 0.0 eV, 5.0 eV, and 8.5 eV.

What is the longest wavelength light capable of ionizing a hydrogen atom in the ground state?

Match the type of system or situation to the appropriate energy level diagram. electronic, vibrational, and rotational states of a diatomic molecule such as O2

Suppose the electron in the hydrogen atom obeyed classical mechanics rather than quantum mechanics. Why should such a hypothetical atom emit a continuous spectrum rather than the observed line spectrum?

Match the type of system or situation to the appropriate energy level diagram. rotational states of a diatomic molecule such as O2

Match the type of system or situation to the appropriate energy level diagram. nuclear (such as the nucleus of a carbon atom)

Given that the wavelength of the observed red band for hydrogen is 656.8 nm with uncertainty 0.11 nm, use the wavelength to calculate the energy of the corresponding photons in electron volts and the uncertainty in transition energy. Use the energy and its uncertainty to determine which transitions (from initial energy level ni to nf) your data is consistent with.

Match the type of system or situation to the appropriate energy level diagram. idealized quantized spring-mass oscillator

Match the type of system or situation to the appropriate energy level diagram. hadronic (such as Δ+)

Match the type of system or situation to the appropriate energy level diagram:electronic states of a single atom such as hydrogen

The Balmer series is a group of spectral lines resulting from the decay of an excited electron in a hydrogen atom to what atomic energy level?a) n = 4b) n = 3c) n = 2d) n = 1

Consider an electron in the state n = 4, l = 3, m = 2, s = 1/2.What is the orbital angular momentum L of this electron?

(a) How many different values of l are possible for an electron with principal quantum number n = 4?(b) How many values of ml are possible for an electron with orbital quantum number l = 4?(c) The quantum state of a particle can be specified by giving a complete set of quantum numbers (n, l, ml, ms). How many different quantum states are possible if the principal quantum number is n = 2?To find the total number of allowed states, first write down the allowed orbital quantum numbers l, and then write down the number of allowed values of ml for each orbital quantum number. Sum these quantities, and then multiply by 2 to account for the two possible orientations of spin.

An electron is trapped in a "quantum well" that confines it to a narrow region in one dimension. The electron's minimum energy is 0.19 meV. What's the width of the well?

Match the type of system or situation to the appropriate energy level diagram. vibrational states of a distomic molecule such as O2

What is the smallest wavelength in the Balmer's series?

What is the largest wavelength in the Balmer series?

What is the smallest value of n for which the wavelength of a Balmer series line is smaller than 400 nm, which is the lower limit for wavelengths in the visible spectrum?

What is the wavelength of the line corresponding to n=5 in the Balmer series?

What is the wavelength of the line corresponding to n=4 in the Balmer series?

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