Читать книгу Quantum Mechanical Foundations of Molecular Spectroscopy - Max Diem - Страница 19

1 What is the maximum wavelength of electromagnetic radiation that can ionize an H atom in the n = 2 state?

2 Why is it that any photon with a wavelength below the limiting value obtained in (1) can ionize the H atom, whereas in standard spectroscopy, only a photon with the correct energy can cause a transition?

3 Assume that you carry out the experiment in (1) with light with a wavelength of 10 nm less than calculated in (1). What is the kinetic energy of the photoelectron created?

4 What is the velocity of the electron in Problem 3?

5 Using the de Broglie relation for matter waves, calculate the velocity to which an electron needs to be accelerated such that its wavelength is 10 nm.

6 What percentage of the velocity of light is the velocity in (5)?

7 What is the relativistic mass of this electron?

8 At what velocity is the wavelength of an electron 30 nm?

9 What is the momentum of such the electron in (8)?

10 What is the mass of a photon with a wavelength of 30 nm?

11 What is the momentum of the photon in (10)?

12 Compare and comment on the masses and momenta of the moving particles in Problems (8)–(11).

13 “Frequency doubling” or “second harmonic generation (SHG)” is a little optical trick (Appendix 3) in which two photons of the same wavelength are squashed into a new photon, while the energy is conserved. Calculate the wavelength of the photon created from frequency doubling of two photons with λ = 1064 nm.

14 “Sum frequency generation (SFG)” is another optical trick (Appendix 3) in which two photons of different wavelengths are squashed into a new photon while the energy is conserved. Calculate the wavelength of SFG photon created from combining two photons with λ1 = 1064 nm and λ2 = 783 nm.

15 The value of the Rydberg constant, Ry, can be calculated according to where e' = e/√4πεo and where mR is the reduced mass of electron and proton. Perform an analysis of the units of Ry.

16 Which two experiments demonstrate that light has wave and particle character?

17 Which two experiments demonstrate that moving electrons have wave and particle character?