4. An H-atom is in is state. a. What is the probability that the electron is found in sphere given by r ≤ ao b. What is (r)? c. calculate (²).
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- 15 b. Suppose an electron is in a spin state given by x = A(). 8i Find i. the normalization constant A ii. (S.) iii. (S.) and iv. the probability that a measurement of S, will yield h/2.7. One electron is trapped in a one-dimensional square well potential with infinitely high sides. a. If you have a probe that has a width for electron detection Ax = 0.00350L in the x direction, for the first excited state ( n =2), what is the probability that the electron is found in the probe when it is centered at x = L/4, (hint: you can use an approximation for this - you do not need to do an integral)? b. What is the average number of electrons that you would detect using the probe described in part "b." centered at x = L/4, ifthe electron is in the first excited state (n = 2) for each experiment and you repeat the experiment N, =100,000 times?Which of these expressions would yield the wavelength of light in meters emitted when an electron drops from orbit n = 3 to n = 2 in a Bohr hydrogen atom? Given h = 4.14 x 10-15 eVs and c = 3.00 x 108 m/s. a. 1.89/hxc b. hc/1.89 c. 1.89 x h x c d. (1.51 + 3.4)/hc e. hc/3.4
- The kinetic energy operator in 3-D is: a. Î= – Invalid element O b. O C. O d. T= ħ2² 2m - ·D2 ħ 2m ħ 2m V VRelative to electrons and electron states, what does the I quantum number specify? Select one: a. The electron shell. b. The number of electron states in each electron subshell. c. The electron subshell. d. The number of electrons. e. The spin moment on each electron.6.An atomic hydrogen atom is immersed in a magnetic field of 12.44 T. For the 2p to 1s transition more than one line will appear due to the Zeeman effect. What is the smallest wavelength separation of these lines? (in units of picometers (pm)).
- 7. For the 3p and 3d states of hydrogen, show that (-) avg =1/1290. ao. n²Which of the following would be closer to the nucleus? a. The ground state (n = 1) of an electron in a singly-charged helium atom. That is, a helium atom with only one electron instead of two. b. Both of these are the same distance from the nucleus c. The ground state electron for the hydrogen.10. If the ground state of an electron in a hydrogen-like atom has an energy of -x eV, which of the following is the energy of one of the excited states? A. -x/9 eV B. -x/2 eV C. -x/3 eV D. - -x/8 eV