Question

Sing the Bohr model, determine the lowest possible energy for the electron in the He⁺ ion.

a) -2.18 × 10⁻18 J
b) -5.45 × 10⁻18 J
c) -1.09 × 10⁻17 J
d) -2.18 × 10⁻17 J

Answer 1

The lowest possible energy for the electron in the He⁺ ion is -5.45 × 10⁻¹⁸ J according to the Bohr model.

Step-by-step explanation:

The energy of an electron in a hydrogen-like ion, such as He⁺, can be determined using the Bohr model.

For a hydrogen-like ion with atomic number Z, the lowest possible energy of the electron can be calculated using the formula:

E = -k·(Z²/n²)·(hc)

where k is a constant (2.179 × 10-18 J), Z is the nuclear charge (+2 in the case of He⁺ ion), n is the principal quantum number (1 for the lowest energy state), and hc is the product of Planck's constant (6.626 × 10-34 J·s) and the speed of light (3.0 × 108 m/s).

Plugging in the values, we can calculate the lowest possible energy for the electron in the He⁺ ion:

E = -2.179 × 10-18 J·(2²/1²)·(6.626 × 10-34 J·s)·(3.0 × 108 m/s)

E ≈ -5.45 × 10-18 J

Therefore, the correct answer is -5.45 × 10-18 J (option b).