Part A What is the lowest possible energy (in electron volts) of an electron in

Question

Part A

What is the lowest possible energy (in electron volts) of an electron in hydrogen if its orbital angular momentum is 6?

E = ? eV

Part B

What is the largest value of the z-component of the orbital angular momentum (in terms of ) for the electron in part A?

Lz = ? h

Part C

What is the smallest value of the z-component of the orbital angular momentum (in terms of ) for the electron in part A?

Lz = ? h

Part D

What is the largest value of the spin angular momentum (in terms of ) for the electron in part A?

S = ? h

Part E

What is the smallest value of the spin angular momentum (in terms of ) for the electron in part A?

S = ? h

Part F

What is the largest value of the orbital angular momentum (in terms of ) for an electron in the M shell of hydrogen?

Lmax = ? h

Part G

What is the smallest value of the orbital angular momentum (in terms of ) for an electron in the M shell of hydrogen?

Lmin = ? h

Explanation / Answer

Part A : The lowest possible energy (in electron volts) of an electron in hydrogen if its orbital angular momentum is 6 would be,

E = 6 x sq.rt.(6.582 x 10^-16) eV = 1.54 x 10^-7 eV

Part B : The largest value of the z-component of the orbital angular momentum (in terms of ) for the electron in part A would be thus,

Lz = 2 h

Part C : The smallest value of the z-component of the orbital angular momentum (in terms of ) for the electron in part A would be,

Lz = -2 h

Part D : The largest value of the spin angular momentum (in terms of ) for the electron in part A would be,

S = =1/2 h

Part E : The smallest value of the spin angular momentum (in terms of ) for the electron in part A would be thus,

S = -1/2 h

Part F : The largest value of the orbital angular momentum (in terms of ) for an electron in the M shell of hydrogen comes out to be,

Lmax = +6 h = 17.5 h

Part G : The smallest value of the orbital angular momentum (in terms of ) for an electron in the M shell of hydrogen thus would be,

Lmin = -6 h

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