No object can travel faster than the speed of light, so itwould appear evident that the uncertainty in the speed ofany object is at most 3 × 108 m s-1.(a) What is the minimum uncertainty in the position of anelectron, given that we know nothing about its speedexcept that it is slower than the speed of light?(b) Repeat the calculation of part (a) for the position of ahelium atom.

Suppose the average distance between the nucleus and the electron in a newly discovered 3s state is given by the ollowing equation: = ° v%47r³ dr, where the wavefunction /3, (r) = r · 3 Зар 27 Ino is independent of 0 and ø. Jse the integral x"e-kz dx = , to determine . Express your final answer in units of the Bohr radius ao and atomic number Z. In other words, if you get a final answer that is 2.3 times , enter 2.3 as your final answer.

One of the emission lines of the hydrogen atom has awavelength of 93.07 nm. (a) In what region of the electromagneticspectrum is this emission found? (b) Determinethe initial and final values of n associated with this emission.

(a) The position of an electron is known to within 14.4 Å (1.44×10- m). What is the minimum uncertainty in its velocity? m s- 1 S (b) Repeat the calculation of part (a) for a carbon atom. ms-1 S

Calculate the de Broglie wavelength of the following. (a) An electron moving at a speed of 1.07×10³ m sl. (b) A proton moving at a speed of 1.07×10³ m s-1. (c) A bullet with a mass of 5.06 grams moving at a speed of 1.02×10³ m s-'. (a) Wavelength electron (b) Wavelength proton (c) Wavelength bullet

5)

Quantum mechanics predicts that the energy of the ground state of the H atom is –13.6 eV. Insight into the magni- tude of this quantity is gained by considering several methods by which it can be measured. (a) Calculate the longest wavelength of light that will ion- ize H atoms in their ground state. (b) Assume the atom is ionized by collision with an elec- tron that transfers all its kinetic energy to the atom in the ionization process. Calculate the speed of the electron before the collision. Express your answer in meters per second (m s-') and miles per hour (miles h-1). (c) Calculate the temperature required to ionize a H atom in its ground state by thermal excitation. (Hint: Recall the criterion for thermal excitation of an oscillator in Planck's theory of blackbody radiation is that hv z kµT.)