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Consider a real system. Assume that a real wavefunction is a combination of two orthogonal functions such that
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Physical Chemistry
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- A normalized wavefunction for a particle confined between 0 and L in the x direction is ψ = (2/L)1/2 sin(πx/L). Suppose that L = 10.0 nm. Calculate the probability that the particle is (a) between x = 4.95 nm and 5.05 nm, (b) between x = 1.95 nm and 2.05 nm, (c) between x = 9.90 nm and 10.00 nm, (d) between x = 5.00 nm and 10.00 nm.arrow_forwardWhich of the following functions can be normalized (in all cases the range for x is from x = −∞ to ∞, and a is a positive constant): (i) sin(ax);(ii) cos(ax) e-x^2? Which of these functions are acceptable as wavefunctions?arrow_forwardNormalize (to 1) the wavefunction e–ax in the range 0 ≤ x ≤ ∞, with a > 0.arrow_forward
- Calculate the energy of the quantum involved in the excitation of (i) an electronic oscillation of period 1.0 fs, (ii) a molecular vibration of period 10 fs, (iii) a pendulum of period 1.0 s. Express the results in joules and kilojoules per mole.arrow_forwardFor the system described in Exercise E7B.1(b) (A possible wavefunction for an electron in a region of length L is sin(3πx/L). Normalize this wavefunction (to 1)), what is the probability of finding the electron in the range dx at x = L/6?arrow_forwardCalculate the size of the quantum involved in the excitation of an electronic motion of frequency 1.0 x 1015 Hz. Ans: 400 kJ/molarrow_forward
- A hydrogen atom rotates in three dimensions at a fixed distance of 100 pm from a fixed point. Ca lculate the energy of the level w ith rotational quantum number J = 1.arrow_forwardBy considering the integral ∫02π ψ*ml ψml dϕ, where ml≠m'l, confirm that wavefunctions for a particle in a ring with different values of the quantum number ml are mutually orthogonal.arrow_forwardThe wavefunction of one of the d orbitals is proportional to sin2θ sin 2ϕ. At what angles does it have nodal planes?arrow_forward
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