ASU BCH 463 (BCH463) Biophysical Chemistry – Module 2 Homework Quiz | Questions & Answers | Latest 2026–2027.

BCH 463: Biophysical Chemistry — Module 2 Homework BCH 463: Biophysical Chemistry — Module 2 Homework 1. A certain wavefunction is zero everywhere except between x=0 and x=L, where it has the constant real value A. What is the value A in nm −1/2 if L is 4 nm? Hint: Use the normalization condition. 2. Write an integral expression for the average value, or expectation value, of the momentum of the ground state. A. L 2 ​ ∫ 0 L ​ sin( L πx ​ )sin( L πx ​ )dx B. L 2 ​ ∫ 0 L ​ sin( L πx ​ )( i ℏ ​ ∂x ∂ ​ )sin( L πx ​ )dx C. L 2 ​ ∫ 0 L ​ sin( L πx ​ )( i ℏ ​ ∂x ∂ ​ )x 2 sin( L πx ​ )dx D. L 2 ​ ∫ 0 L ​ sin( L πx ​ )xsin( L πx ​ )dx 3. Write an integral expression for the probability of finding the particle in the state n between x=0 and x=L/4. A. L 2 ​ ∫ 0 L/4 ​ sin( L nπx ​ )dx B. L 2 ​ ∫ 0 L/4 ​ sin 2 ( L nπx ​ )dx C. L 2 ​ ∫ 0 L/4 ​ xsin( L nπx ​ )dx D. L 2 ​ ∫ 0 L/4 ​ xsin 2 ( L nπx ​ )dx 4. What is the ionization energy of Li²⁺ in eV? 5. Calculate the probability that a particle in a one-dimensional box of length a is found to be between 0 and a/2. A. 0.3 B. 0.6 C. 0.5 D. 0.4 6. For a one-dimensional particle in a box, what is the wavelength of the first excited state in terms of L? A. L B. L/2 C. 2L/3 D. 2L 7. In quantum mechanics, suppose that a ball is in a well. Next to this well is a second well with a finite barrier separating the two wells. If the kinetic energy of the ball is less than the potential energy needed to travel over the barrier, the ball will: A. Always be found in the first well. B. Always be found in the second well. C. Have a probability between 0 and 1 of being found in each well. D. Have a probability between 1 and 2 of being found in each well. 8. For a one-dimensional particle in a box, if the potential at x=c is infinity, then the wavefunction at x=c must be: A. A positive number greater than 1 B. 1 C. 0 D. A positive number less than 1 9. For a one-dimensional particle in a box, the probability of finding the particle within the box is: A. 0 B. 0.25 C. 0.5 D. 1 10. For a particle in a one-dimensional box, the energy of the wavefunctions: A. Decreases according to n B. Decreases according to n 2 C. Increases according to n 2 D. Increases according to n 11. For a particle in a box, the wave functions: A. Always are zero at x=L/2 B. Must have a positive slope at x=L C. None of the above D. Always are non-zero at x=L/2 12. For the one-dimensional particle in a box of length L=1 Å. Calculate the numerical probability of finding the particle between 0 and L/4, for the ground state. A. 0.091 B. 0.103 C. 0.072 D. 0.272 13. Calculate the frequencies of radiation emitted in the transitions (n=102→n=100) for the hydrogen atom. A. 1.36×10 10 Hz B. 1.60×10 19 Hz C. 5.28×10 5 Hz D. 1.27×10 10 Hz 14. Calculate the ionization energy of the hydrogen atom. A. None of above B. 27.2 eV C. 6.8 eV D. 13.6 eV 15. For an electron in a box of length L=1 nm, find the energy of the first excited state in eV. 16. Calculate the probability of finding the particle in the first excited state (n=2) in the range 0xL/2 for a box of length L. 17. Given an electron in a box with L=2 nm, calculate the wavelength (in nm) of the photon emitted when the electron transitions from the third excited state (n=4) to the ground state (n=1). 18. A possible wavefunction for an electron in a region of length L (from x=0 to x=L) is sin(3πx/L). Normalize the wavefunction. A. The wavefunction cannot be normalized. B. L 2 ​ ​ C. L 2 ​ D. L 3 ​ ​ 19. What does an expectation value ⟨x⟩ of the position operator for a wave function ψ(x) tell you? A. The least likely place to find particle. B. The average value of the position you would get if you measure it multiple times. C. The position of where the particle actually is. D. The most likely place to find particle. E. The value where the Hamiltonian must be evaluated to get the energy. 20. In the particle-in-a-box scenario, if the length of the box is 10 nm and there are 6 electrons, calculate the longest wavelength transition in nm for an electron. 21. Calculate the wavelength associated with a 1 eV photon in micrometers. 22. Calculate the wavelength associated with a 1 eV electron in Angstroms. 23. A particle in a one-dimensional box is confined to the interval [−a/2,a/2] and is in its first excited state. Calculate the probability of finding the particle in the subinterval (0,a/4).