The uncertainty principle 1. calculate the minimum uncertainty in the speed of an electron in a one-dimensional region of length 2ao, where an is the bohr radius (53 pm). 2. calculate the minimum uncertainty in the position of a 1.0 g particle whose speed is known to within 1x10-6 m-s-1 and comment on whether this uncertainty in position is physically meaningful for a 1.0 g particle. (for reference, a 1.0 g cube of aluminum would have an edge length of 0.72 cm.) conjugate variables 3. show whether the operators a = 3x and b = x-1 commute. (use the general function f( 4. show that x and px do not commute using the function sin" application 5. following the example we did in class for determining the radius of the electron's orbit in the lowest energy state of hydrogen, determine the radius for a li-ion. note the numerator in the coulombic term indeed changes, but not by multiplying by another e! what happens for het, in fact, is that the q (charge) term for the nucleus is +2 so the coulombic term is 4.92 - (-e)(+2e), -2e2 4150 4150 4180