2) Suppose an electron in a hydrogen atom is prepared as a superposition of two

Question

2) Suppose an electron in a hydrogen atom is prepared as a superposition of two states, ?1 with E1 = -13.6 eV and ?2 with E2 = -3.4 eV. The superposition is ? = (?1 + 3?2) /v10. If the energy of the electron is measured, which of the following values is a possible result of this measurement?

-3.06 eV
-3.4 eV
-4.42 eV
-10.2 eV
-17 eV

3) If an electron in a hydrogen atom is in a state with orbital angular momentum number l = 0, which of these statements is true:

Its wave function's angular dependence depends on the value of its principal number n.
Its wave function's angular dependence depends on the value of its magnetic number m.
Its wave function is always spherically symmetric

Explanation / Answer

1) Solutions of the Schrodinger equation in a hydrogen atom are characterized by their principal number n, their orbital angular momentum number l and their magnetic (azimuthal) number m. There are certain rules about the range of these numbers. Which of the combinations of (n,l,m ) below does not satisfy these rules, and is thus impossible?

The impossible state is described by :

(n,l,m ) = ( 4,3,0 )
(n,l,m ) = ( 4,3,3 )
(n,l,m ) = ( 3,2,1 )
(n,l,m ) = ( 3,3,2 )
(n,l,m ) = ( 3,2,0 ) Answer: The possible values of l are 0 to (n-1) The possible values of m1 are -l to + l. (n,l,m ) = ( 4,3,0 )   possible
(n,l,m ) = ( 4,3,3 )   possible
(n,l,m ) = ( 3,2,1 )   possible
(n,l,m ) = ( 3,3,2 ) not possible   because for n=3 the possible values of l are 0,1,2.
(n,l,m ) = ( 3,2,0 )   possible. Note: Please submit one question per post as per rules.

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