Download Problems and Questions on Lecture 2 Useful equations and

Problems and Questions on Lecture 2
Useful equations and constants
1.
2.
3.
4.
5.
6.
7.
8.
Neutrons have a:
(A) positive charge and a mass approximately equal to a proton.
(B) positive charge and a mass approximately equal to an electron.
(C) neutral charge and a mass approximately equal to a proton.
(D) neutral charge and a mass approximately equal to an electron.
(E) negative charge and a mass approximately equal to a proton.
Rutherford’s Gold Foil experiment caused a modification of which of the following?
(A) Plum-pudding model of the atom
(B) Planetary model of the atom
(C) de Broglie hypothesis
(D) Wave nature of light
(E) Quantum theory of light
In Rutherford’s Gold Foil experiment, most of the alpha particles passed through the foil undeflected. Which of the
following properties of the atom can be explained from this observation?
(A) The atom’s negative charge is concentrated in the nucleus.
(B) The nucleus has electrons and protons.
(C) The atomic mass is distributed evenly throughout the atom.
(D) The alpha particles can’t be deflected by electrons.
(E) The size of the nucleus is much less than the size of the atom.
According to the Bohr model of the atom, the angular momentum of an electron is:
(A) Linearly increases with increasing electron’s velocity
(B) Linearly increases with increasing orbital radius
(C) Quantized
(D) Inversely proportional to the electron’s velocity
(E) Inversely proportional to the orbital radius
When an electron falls from an orbit where n = 2 to n = 1:
(A) A photon is emitted
(B) A photon is absorbed
(C) No change in atomic energy
(D) Atomic energy decreases to zero
(E) Atomic energy increases
When an electron jumps from an orbit where n = 1 to n = 3 its orbital radius in terms of the smallest radius r 1 is:
(A) r1/9
(B) r1/3
(C) 2 r1
(D) 3 r1
(E) 9 r1
When an electron jumps from an orbit where n = 1 to n = 4 its energy in terms of the energy on the ground level is:
(A) E1/9
(B) E1/16
(C) 2 E1
(D) 4 E1
(E) 16 E1
An electron is moving around a single proton in an orbit characterized by n = 5. How many of the electron's de Broglie
wavelengths fit into the circumference of this orbit?
(A) 3; (B) 4; (C) 5; (D) 16; (E) 25
9.
According to the classical theory of electro-magnetism an electron orbiting the atomic nucleus is:
(A) Changes its energy by certain portions
(B) Conserves its angular momentum
(C) Conserves its energy
(D) Radiates its energy and falls on the nucleus
(E) Changes its angular momentum by certain portions
10. In the hydrogen atom an electron is excited to an energy level n = 4 then it falls down to the level n = 2.
a. What is the wavelength of the emitted photon?
b. What type of electromagnetic radiation is this photon associated with?
c. What is the next possible transition?
d. What is the wavelength associated with this transition?
Answer: a) 488 nm; b) Visible light-green; c) 2→1; d) 122 nm
11. The electron in a hydrogen atom has an energy of -13.6 eV on the ground level.
a. Calculate the first five energy levels (n=1 to n=5).
b. Draw the energy diagram including the ground level.
c. The electron is on the n=4 level; draw all possible transitions.
Answer: a) 1st -13.6 eV;
2nd
-3.4 eV;
3rd
-1.51 eV;
4th
-0.85 eV;
5th
-0.54 eV
b)
c)
12. In the hydrogen atom an electron is excited to an energy level n = 5 then it falls down to the level n = 3.
a. What is the wavelength of the emitted photon?
b. What type of electromagnetic radiation is this photon associated with?
c. What are the next possible transitions?
d. What are the wavelengths associated with these transitions?
Answer: a) 1.29x10-6 m; b) Infrared radiation; c) 3→2, 3→1, 2→1; d) 3→2: 661 nm;
3→1: 103 nm;
2→1: 122 nm.
13. The electron in a helium atom has an energy of -54.4 eV on the ground level.
a. Calculate the first five energy levels (n=1 to n=5).
b. Draw the energy diagram including ground level.
c. The electron is on the n=3 level; draw all possible transitions.
Answer: a) 1st -54.4 eV
2nd
3rd
4th
5th
-13.6 eV
-6.04 eV
-3.40 eV
-2.18 eV
E = -54.4 eV
1
b)
n=3
n=2
n=1
c)
14. The atomic energy levels can be determined by the following formula E n = Z2E1/n2 where Z = atomic number; E1 = 13.6eV (ground state of the hydrogen atom, n=1).
a.
b.
c.
d.
What are the energy levels, for n=1, 2, 3 and 4 of the hydrogen atom?
What is the frequency of the emitted photon if an electron makes a transition from the n = 3 level to the n
= 2 level?
What is the wavelength of the photon for the same transition?
Would the emitted photon be visible?
Answers: a) –13.6eV, –3.40eV, –1.51eV, –0.85eV ;
b)
Hz;
c) 658nm;
d) Yes – red light
15. The atomic energy levels can be determined by the following formula E n = Z2E1/n2 where Z = atomic number; E1 = 13.6eV (ground state of the hydrogen atom, n=1).
a.
b.
c.
d.
What are the energy levels, for n=1, 2, 3 and 4 of the singly ionized (only one electron present) helium
atom (Z=2)?
What is the frequency of the emitted photon if an electron makes a transition from the n = 4 level to the n
= 2 level?
What is the wavelength of the photon for the same transition?
Would the emitted photon be visible?
Answers: a) –54.4eV, –13.6eV, –6.04eV, –3.40eV; b)
Hz; c)
m; d) No – Ultraviolet
16. Which of the following statement(s) can be associated with Bohr’s theory of the atom?
I.
An electron orbiting the nucleus can change its energy continuously.
II.
An electron orbiting the nucleus emits energy and falls into the nucleus.
III.
An electron orbits the nucleus without radiating energy and can change its energy only by a specific,
quantized amount, when it moves between the orbits.
IV.
Electrons can only orbit the nucleus in specific circular orbits with fixed angular momentum and
energy.
(A) I and II
(B) II and IV
(C) II and III
(D) III and IV
(E) I, II, III and IV
17. When an electron falls from an orbit where n = 2 to n = 1:
(A) A photon is emitted.
(B) A photon is absorbed.
(C) No change in atomic energy. (D) The
atomic energy decreases to zero. (E) The atomic energy increases.
18. When an electron jumps from an orbit where n = 1 to n = 4, its energy in terms of the energy of the ground level (E 1) is:
(A) E1/9
(B) E1/16
(C) 2 E1
(D) 4 E1
(E) 16 E1
19. Which of the following is a limitation of the Bohr Model of the atom?
(A) It does not explain atomic spectra.
(B) It successfully predicts the intensity of the photons emitted when electrons change energy levels.
(C) The model only applies to Hydrogen like atoms.
(D) The model only applies to light atoms.
20. Which of the following transitions is related to the energy absorption?
(A) α1
(B) α2
(C) α3
(D) α4
(E) α5
21. A free electron is captured by a proton. As a result of this process two
photons are emitted. The energy of the first photon is E 1 = 3.4 eV.
a. Calculate the wavelength of the photon with energy E1.
b. Calculate the energy of the second photon E2.
c. Calculate the wavelength of the second photon?
d. On the diagram below show arrows associated with these
transitions of the electron.
The electron stays on the ground level for a long limit of time and then
absorbs an energy of 15 eV from an incident photon.
e. What is the energy of the emitted electron?
f. What is the De Broglie wavelength of the emitted electron?
Answer: a. λ = 365 nm; b.E = 10.2 eV; c. λ = 122 nm; d. An arrow from 0 eV to -3.4 eV and another arrow from -3.4 eV to -13.6
eV; e. E = 1.4 eV or 2.24 x 10-19 J; f. λ = 1 nm
22. Calculate the energy of a photon released from each of these energy level transitions, in a hydrogen atom: a) n = 2 to n =
1; b) n = 3 to n = 1;
c) n = 5 to n = 1; d) n = 5 to n = 2 e) n = 5 to n = 3
23. What is the minimum amount of energy needed to ionize a hydrogen electron in these levels:
a) n=1;
b) n=3;
c) n=6;
24. What color photons are emitted by a hydrogen atom in each energy level drop?
a) n = 3 to n = 2; b) n = 4 to n = 2; c) n = 5 to n = 2; These are the three visible spectral lines of hydrogen.
25. Using Wilson-Summerfeld quantization rule, calculate energy of a particle in a cubic box, and then calculate degenerate
and non degenerate energy levels of the particle for sum of the quantum numbers
.
26. Using Wilson-Summerfeld quantization rule, calculate energy of a 1D harmonic oscillator. (Hint:
)
27. Using Wilson-Summerfeld quantization rule, calculate energy of a 2D harmonic oscillator, and then calculate degenerate
and non degenerate energy levels of the particle for sum of the quantum numbers
.
28. Using Wilson-Summerfeld quantization rule, calculate energy of a 3D harmonic oscillator, and then calculate degenerate
and nond egenerate energy levels of the particle for sum of the quantum numbers
.
29. Using Wilson-Summerfeld quantization rule, calculate energy of a particle in a rigid rotator.