By D.R. Bates

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2 XY Z ∂ 2 XY Z ∂ 2 XY Z 2m + + + 2 E (XY Z) = 0. 34) Since Y Z is not a function of x , XZ is not a function of y , and XY is not a function of z, we can remove them from the derivatives to give YZ ∂ 2X ∂ 2Y ∂ 2 Z 2m + XZ + XY + 2 E (XY Z) = 0. 35) If Eq. 35) is divided by XY Z , we obtain 1 ∂ 2Y 1 ∂ 2Z 2m 1 ∂ 2X + + = − 2 E. 36) Since each term on the left-hand side of Eq. 36) is a function of only one variable, each will be independent of any change in the other two variables. Each term must be equal to a constant, which we will call −k 2 .

00% of the speed of light? 3. 0 nm. A scattered photon having a wavelength of 200 nm is observed after the collision. What will be the velocity and de Broglie wavelength of the ejected electron? 6 The Heisenberg Uncertainty Principle 19 4. The work function of a metal is the energy required to remove an electron from the metal. 60 × 10−12 erg)? 5. For Be3+ , calculate the wavelength of the photons emitted as the electron falls from n = 3 to n = 2 and from n = 4 to n = 3. 6. 8 nm. (a) What is the frequency of this spectral line?

11. Neutrons having energies equivalent to the kinetic energy of gaseous molecules at room temperature (kT ) are called thermal neutrons. What is the wavelength of a thermal neutron at 27◦ C? 12. Suppose an electron remains in an excited state of an atom for 10−8 s. What would be the minimum uncertainty of the energy of the photon emitted as the electron falls to the ground state? What uncertainty in the wavelength of the photon does this correspond to? 20 Chapter 1 The Early Days 13. 6 eV. 300 nm passes through water and is completely absorbed by ionizing water molecules, how many molecules could the photon ionize?