The ionization potential of an electron in an atom or molecule is the energy req

Question

The ionization potential of an electron in an atom or molecule is the energy required to remove the electron. Calculate the ionization potential for a Is electron in He^+. Enter the answer in eV (electronvolt), to two significant figures and do not enter the units. Note that even though the Bohr model is wrong it gives the same result as quantum mechanics for the energies of one electron atoms. So the Rydberg equation holds but R_Hc+ (rydberg constant for He^+) = 109752 cm^-1. A free electron corresponds to n = infinity and Is in He^+ is the ground state (lowest energy state, n = 1). Also, 1 eV = 8065.73 cm^-1.

Explanation / Answer

we know that

1/wave length = RHe+ x Z^2 [ ( 1/n1)^2 - (1/n2)^2]

here

n1 = 1

n2 = infinity

so

atomic number (Z) for He+ = 2

so

1 / wavelenght = RHe+ x 4 [ ( 1/1)^2 - (1/infinity)^2]

1/wave length = 4 x RHe+ [ 1- 0]

1/wave length = 4 x RHe+

1/wave length = 4 x 109752 cm-1

now

given that

1 eV ----> 8065.73 cm-1

let

y eV ---> 4 x 109752 cm-1

y = 4 x 109752 / 8065.73

y = 54.43

since energy is released , it should be negative

so

the ionization potential is -54.43 eV

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.