For this problem, you will consider a 4-dimensional hilbert space. the basis vectors |x) are orthonormal. consider the three state vectors defined below: a. rank the normalization constants by magnitude from largest to smallest. show your work b. evaluate the espression (c|a). show your work. a different vector is defined by the following expression, where γ is an determine the value of γ such that state vector d is orthogonal to state vector a. show your work c.

Use henry's law and the solubilities given below to calculate the total volume of nitrogen and oxygen gas that should bubble out of 1.7 l of water upon warming from 25 ˚c to 50 ˚c. assume that the water is initially saturated with nitrogen and oxygen gas at 25 ˚c and a total pressure of 1.0 atm. assume that the gas bubbles out at a temperature of 50 ˚c. the solubility of oxygen gas at 50 ˚c is 27.8 mg/l at an oxygen pressure of 1.00 atm. the solubility of nitrogen gas at 50 ˚c is 14.6 mg/l at a nitrogen pressure of 1.00 atm. assume that the air above the water contains an oxygen partial pressure of 0.21 atm and a nitrogen partial pressure of 0.78 atm.