The ionisation energy of He+ = 19.6 multiplied by 10^-18 J atom^-1 . Energy of the first stationary state of Li^2 is what?

To find the energy of the first stationary state of Li²⁺, we can use the concept of ionization energy and the relationship between the energy levels of hydrogen-like ions. Since Li²⁺ is a hydrogen-like ion with a charge of +3 (because lithium has three protons), we can apply the formula for the energy levels of such ions.

Energy Levels of Hydrogen-like Ions

The energy of the nth stationary state of a hydrogen-like atom can be calculated using the formula:

E_n = -\frac{Z^2 \cdot R_H}{n^2}

Where:

• E_n = energy of the nth level
• Z = atomic number (for Li, Z = 3)
• R_H = Rydberg constant for hydrogen (approximately 2.18 x 10^-18 J)
• n = principal quantum number (for the first stationary state, n = 1)

Calculating the Energy for Li²⁺

Now, substituting the values into the formula:

E_1 = -\frac{3^2 \cdot 2.18 \times 10^{-18}}{1^2}

Calculating this gives:

E_1 = -\frac{9 \cdot 2.18 \times 10^{-18}}{1}

Now, performing the multiplication:

E_1 = -19.62 \times 10^{-18} J

Final Result

Thus, the energy of the first stationary state of Li²⁺ is approximately:

E_1 ≈ -19.6 x 10^-18 J

This result shows that the energy level of Li²⁺ is quite similar to that of He⁺, which makes sense given that both are hydrogen-like ions, but with different nuclear charges. The negative sign indicates that the electron is bound to the nucleus, and energy must be supplied to remove it from the atom.