Atomic packaging
1. What does an atom look like?
Solution:
Aristotle (384 BC): Matter is continuous, it can be divided infinitely. Leucippus, Democritus (5th century BC): Matter is discontinuous, composed of indivisible particles – atoms. J.J. Thomson (1856–1940) created the so-called “plum pudding model”. The atom is a positively charged sphere in which electrons float. E. Rutherford (1871–1937) created the “planetary model of the atom”. The entire mass of the atom (as well as its positive charge) is concentrated in the nucleus (10–15m). Around the nucleus, electrons orbit in circles (ellipses – A. Sommerfeld). The radius of the atom is about 10–10m. The main shortcoming of this model was that when orbiting the nucleus, the electron would lose energy, its speed would decrease, it would spiral inward and fall into the nucleus. The material world could not exist. N. Bohr (1883–1962) created the “quantum model of the atom”.
- a.) An electron can move around the nucleus only along specific circular paths called orbitals (energy levels). The length of an orbital equals an integer multiple of the wavelength of the de Broglie wave corresponding to the electron.
- b.) If the electron moves along an orbital, it does not emit energy
- c.) When the electron transitions from one orbital where it had energy En to another orbital with lower energy Em, it emits one light quantum – a photon. K. Heisenberg (1901–1976), E. Schrödinger (1887–1961) created the “quantum mechanical, probabilistic model”. It is not possible to determine both the position and velocity of an electron with equal precision. One can determine regions where the electron may be found with a certain probability around the nucleus.
2. What properties does the hydrogen atom have in Bohr's model?
Solution:
3. How long does it take light to pass through an atom with a radius r = 3.10–10m?
Solution:
Analysis:
Light passes through the atom in t = 2.10–18s.
4. Calculate the ground state energy of the hydrogen atom E1. 1J = 0.6242.1019 eV
Solution:
The ground state energy of the hydrogen atom is E1 = –13.6eV.
5. Calculate the energies of the hydrogen atom in stationary orbits with principal quantum number n = 1,2,3,4,5,6. The energy of the first orbit is E1 = –13.6 eV. (Example 4)
Solution:
6. Calculate the velocities of the electron on individual orbitals in the hydrogen atom, knowing that
r1 = 0.53.10–10m.
Solution:
Analysis:
7. Determine the frequency of the visible lines of the Balmer series (J. Balmer, 1825–1898) for hydrogen. The series arises from electron transitions to the second orbit.
Solution:
Analysis:
E1 = –13.6eV, E2 = –3.4eV, E3 = –1.5eV,
E4 = –0.85eV, E5 = –0.544eV, E6 = –0.378eV
8. A hydrogen atom in the ground state absorbed energy of 10.2eV. To which energy level did the electron transition?
Solution:
Analysis:
ΔE = 10.2eV, E1 = –13.6eV, n = ?
The electron transitioned to the second energy level.
9. A helium–neon laser has power of 2mW and emits radiation with wavelength 632.8nm. Determine the energy, mass and momentum of the emitted photons.
Solution:
Analysis:
P = 2.10–3W, λ = 632.8.10–9m, E = ?, m = ?, p = ?
A photon has energy E = 3.14.10–18J, mass m = 3.49.10–36kg and momentum p = 1.05.10–27kg·m·s–1.
10. The hydrogen atom transitions from stationary state n = 6 to state m = 1. Calculate the frequency and wavelength of the emitted photon. Use the Rydberg formula. (J.R. Rydberg 1854–1919)
Solution:
Analysis:
n = 6, m = 1, R = 3.29.1015s–1
The emitted photon has frequency f = 3.199.1015 Hz and wavelength λ = 9.38.10–8m.
11. Calculate the amount of electromagnetic energy emitted by a hydrogen atom if its electron jumps from the first orbital to an infinitely distant orbital.
Solution:
Analysis:
The hydrogen atom emits –13.6eV of electromagnetic energy.
12. Derive the Rydberg constant R
Solution:
