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
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- What is the correct expression for the wave function of the 1s orbital of a hydrogen atom? Question 14 options: W- 1/(па03). е-г/a0 Ф- 1/(пао3)1/2. e-r/a0Ҹ- 1/(па03)1/2. e-2r/a0 W- 1/(па0з). е-2r/a0(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
- -7 For hydrogen atom electron, with Spin , in the state a -A(), Determine A, , of Sx, Sy,S2 13217水 and with spin State x く>,くら、?,くら,>, andWhich 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/No3. 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.