A hydrogen atom is in the 4d state. a) What is the magnitude of the orbital angular momentum? b) Calculate the possible values of the total angular momentum quantum number. Calculate the magnitude of the total angular momentum for each value in (b). c)
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- Normalize the wavefunction for the 2s orbital of a hydrogen electron. 3 Rn. 1 (r) = = (²/7) ² (2 − p) e - ² - a 2Zr na(a) For the 1s wave function, calculate the probability for the electron to be found within the nucleus, considered to be a sphere of radius R. (b) Evaluate the probability for a nucleus of lead (R = 7.1 fm). (c) Suppose instead that a muon (m = 207m) were in its 1s state. What is the probability to find it inside the lead nucleus?None
- 3. Suppose an electron in a hydrogen atom is in a 2p state, and the radial wavefunction is (2a.)3/2 /3a. 2ao , where a, is the Bohr radius. (a) 2-axis? What possible angles might the angular momentum vector L make with the (b) What is the most probable radius (in terms of a,) at which the electron is found? (c) What is the expectation value of r in this state? Note: xe-"dx = 120. (p) S° x*e-dx = 23.91. What is the probability of finding such an electron between a, and oo? Note:An electron is known to have an energy level of 5. What are the possible values for its angular momentum quantum numbers? Explain your answerWhich of the following sets of quantum numbers n, l, and m¡ would be possible for an excited state of hydrogen? (circle yes or no) I. n= 4, 1= 2, mị II. n= 3, 1=2, m¡ = -2 П. п %3D 2, 1%32, т) %3D+1 IV. п %3D17, 1 %3 2, т %3 —2 =-3 Yes/No Yes/No Yes/No Yes/No
- 3. Suppose an electron in a hydrogen atom is in a 2p state, and the radial wavefunction e 2ao, where a, is the Bohr radius. 1 is (2ао)3/2 VЗа. (а) What possible angles might the angular momentum vector L make with the Z-axis? (b) What is the most probable radius (in terms of a.) at which the electron is found? (c) What is the expectation value of r in this state? Note: S xe-"dx 120. (d) What is the probability of finding such an electron between a, and ∞? Note: ° x*e-"dx = 23.91.When an excited hydrogen atom returns to the ground state light of wavelength λ = 102.5 nm is emitted. The Rydberg constant is R = 1.097 x 107 m-1. What was the principle quantum number n of the excited state? Select one: a. 3 b. 2 c. 5 d. 4