## Inertial Reference Frames

Calculate the quantum number for a glycerol droplet with a radius of 1.2 μm while it moves in a 22 μm long box at a speed of 1.2 μm/s. (Assume the density of glycerol is 1261 kg/m^{3}).

6.53×10^{16}

5.22×10^{17}

7.23×10^{8}

2.55×10^{8}

Determine the ionization energy of a hypothetical element that exhibits the energy levels shown in the figure below.

1.8 eV

2.8 eV

3.6 eV

8.2 eV

An 18-nm long box, divided into 3-nm and 15-nm sections by a removable partition, contains an electron at its third energy level (n=2) inside the smaller region. After temporary partition removal and reinsertion, the electron is in the larger section. What's its new quantum state?

10

20

25

30

An electron has the following energies: (i) 0.60 eV, (ii) 1.40 eV, and (iii) 1.80 eV. Determine the penetration distance for this electron in a potential well of depth U_{0}=4.00 eV.

(i) 0.105 nm (ii) 0.121 nm (iii) 0.131 nm

(i) 0.121 nm (ii) 0.105 nm (iii) 0.141 nm

(i) 0.105 nm (ii) 0.121 nm (iii) 0.161 nm

(i) 0.151 nm (ii) 0.121 nm (iii) 0.105 nm

In a rigid box with a length of L = 1.00 nm and for the quantum state with quantum number n=4, where is the particle most likely to be found along the box's length?

1/8 nm, 3/8 nm, 5/8 nm, 7/8 nm

1/4 nm, 1/2 nm, 3/4 nm

1/8 nm, 2/8 nm, 3/8 nm, 4/8 nm

1/4 nm, 3/2 nm, 7/4 nm

A molecule with O-H bond absorbs infrared light at a wavelength of 2.9 micrometers (μm). Calculate the energy for the first three states of vibration for this O-H bond.

E_{0}=0.21 eV , E_{1}= 0.64 eV, E_{2}=1.1 eV

E_{0}=0.21 eV , E_{1}= 0.71 eV, E_{2}=1.0 eV

E_{0}=0.21 eV , E_{1}= 0.58 eV, E_{2}=1.1 eV

E_{0}=0.21 eV , E_{1}= 0.64 eV, E_{2}=1.2 eV

An electron is confined within a one-dimensional rigid box with a length of 0.159 nm, approximately thrice the Bohr radius. Determine the three lowest electron energy levels.

E_{1}= 14.9 eV, E_{2}=60 eV, E_{3}=104 eV

E_{1}= 60 eV, E_{2}=14.9 eV, E_{3}=134 eV

E_{1}= 60 eV, E_{2}=134 eV, E_{3}=14.9 eV

E_{1}= 14.9 eV, E_{2}=60 eV, E_{3}=134 eV

Identify the wavelengths in the atom's emission spectrum due to quantum shifts between its three lowest energy states. Considering the atom as an electron trapped in a one-dimensional box of 0.159 nm, about three times the Bohr radius. Label each wavelength as λ_{n→m} to indicate the specific transition.

λ_{2→1 }= 28.0 nm, λ_{3→1 }= 10.0 nm, λ_{3→2 }= 20.0 nm

λ_{2→1 }= 10.0 nm, λ_{3→1 }= 27.0 nm, λ_{3→2 }= 17.0 nm

λ_{2→1 }= 17.0 nm, λ_{3→1 }= 10.0 nm, λ_{3→2 }= 27.0 nm

λ_{2→1 }= 28.0 nm, λ_{3→1 }= 10.0 nm, λ_{3→2 }= 17.0 nm

Consider a particle confined along the y direction and characterized by the following wave function:

Ψ(y)=Ψ_{0}√(1 -y^{2}/4 mm ^{2}) if |y| ≤ 2.0 mm and Ψ(y)=0 if |y| ≥ 2.0 mm.

Determine the probability of locating the particle within a distance of 0.50 mm from y=0.0 mm.

38 %

52 %

60 %

72 %

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