Question

Hydrogen atom number 1 is known to be in the 4f state. Hydrogen atom number 2 is in the 5d state.

Required:
a. What is the energy of the atom?
b. WHat is the magnitude of this atom's orbital angular momentum?
c. Hydrogen atom number 2 is in the 5d state. Is this atom's energy greater than, less than, or the same as that of atom 1? Explain.
d. Is the magnitude of the orbital angular momentum of atom 1 greater than, less than, or the same as that of atom 2? Explain.

Answer 1

Answer:

4f   E₄ = 0.85 eV,    L₄ = 4.22 10⁻³⁴ ,  

5d          E₅ = 0.544 eV ,    L5 = 5.28 10⁻³⁴

Explanation:

Let's use the Bohr model, stable the energy of the hydrogen atom

              E = -13.606 / n2

where Eo = 13.606 eV is the energy of the ground states.

a) the energy of each atom

level 4f

In this nomenclature enumeration is the number n

               E = -13606 / 42

               E₄ = 0.85 eV

level 5d

                E₅ = -13.606 / 5 2

                E₅ = 0.544 eV

b) The angular momentum is given in Boh's model

                     L = n h / 2pi

let's calculate

             

level 4f             L₄ = 4 6.63 10⁻³⁴-34 / 2 pi

                        L₄ = 4.22 10⁻³⁴

level 4d

                       L5 = 5 6.63 10-⁻³⁴ / 2pi

                       L5 = 5.28 10⁻³⁴

c) The hydrogen atom in state n = 5 has lower energy than the other state

d) Atom 1 has less angular momentum than atom 2