Section   9.2The Dual Nature of Light

1. (Exercises 1 and 2) A laser is a device that produces a very bright, coherent beam of light that is composed of photons that all have the same frequency. If a certain laser produces light with a frequency of 3.25 x 10¹⁵ Hz in the ultraviolet portion of the spectrum, what is the energy associated with each photon?

In this case the frequency is directly related to the energy, and we can use Planck's quantum equation to find the energy. (Recall that Hz is equivalent to 1/s.)

E = h f = (6.63 x 10^-34 J-s) (3.25 x 10¹⁵ Hz) =
2.15 x 10^-18 J

Section   9.3Bohr Theory of the Hydrogen Atom

2. (Exercises 7 and 8) Given an electron in the hydrogen atom that is in the energy level designated by the principal quantum number n = 5:, determine the energy of this electron while it occupies this orbit.

The energy of an electron in the hydrogen atom is related to the ground state energy by the relationship:

E_n = -13.60 eV / n²

For the n = 5 level, the electron's energy will therefore be:

E₅ = -13.60 eV / (5)² = -13.60 eV / 25 = -0.54 eV

Section   9.6Matter Waves

3. (Exercises 11 and 12) What is the de Broglie wavelength for a rifle bullet with a mass of 0.00200 kg that is traveling with a speed of 120 m/s?

The de Broglie wavelength is given by the equation:

= h / mv = 6.63 x 10^-34 J-s / (0.00200 kg) (120 m/s) = 2.76 x 10^-33 m

This wavelength is much too short to produce easily seen effects in our study of objects even as small as a rifle bullet.

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