The orbital frequency of an electron in a hydrogen atom is proportional to (n is the principal quantum no.) (a) n-3 (b) n? (c) n-2 (d) n³
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- 1) A wave function for an excited state of the hydrogen atom is given by 2 1 = sh Απαβ sin? @ exp (-i2ф). 3ao exp Зао Apply the angular momentum operators 1 Î? = - h? sin 0 - ih- + = - sin 0 d0 sin? 0 dp² to find:- i) the value of the orbital angular momentum quantum number, 1. ii) the quantum number for the z-component on the orbital angular momentum, mj.The orbital radii of a hydrogen-like atom is given by the equation What is the radius of the first Bohr orbit in (a) He+,(b) Li2+, and (c) Be3+The quantum mechanical model of the hydrogen atom requires that if the principal quantum number is 4, there will be how many different permitted orbital quantum number(s)? Oone Otwo O four five!
- Which 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/NoSuppose an electron has magnetic quantum number ml = 1. What constraints are on the values of the other quantum numbers (orbital l and principal n) for an electron in an atom? n > l ≥ 1 l ≥ n ≥ 1 l ≤ 1, n ≤ 2 l ≤ 2, n ≤ 1 There are no constraints.An electron is in the third excited orbit of hydrogen, corresponding to n = 4. (a) Find the radius of the orbit. nm (b) Find the wavelength of the electron in this orbit. nm