The Bohr model gives the value for the ionization potential of Be⁺⁺⁺ ion as__________10^-1 eV
(Round off to two decimal places)
Correct answer is between '21.74,21.78'. Can you explain this answer?

Question

The Bohr model gives the value for the ionization potential of Be+++ion as__________10-1 eV(Round off to two decimal places)Correct answer is between '21.74,21.78'. Can you explain this answer?

Answer

The Bohr model and the ionization potential of Be ion:

The Bohr model is a simplified model of the atom proposed by Niels Bohr in 1913. It describes the structure of the atom using quantized energy levels and orbits. The ionization potential is the energy required to remove an electron from an atom or ion, resulting in the formation of a positive ion.

The ionization potential of an atom or ion can be calculated using the formula:

Ionization Potential = E_n - E_m

where E_n is the energy of the electron in the initial energy level and E_m is the energy of the electron in the final energy level.

Determining the ionization potential of Be ion using the Bohr model:

1. The Bohr model represents the electron orbits as circular paths around the nucleus. The energy of an electron in a particular orbit is given by the formula:

E_n = -13.6 eV/n²

where E_n is the energy of the electron in the nth orbit and n is the principal quantum number.

2. The Be ion has a charge of +2, indicating that it has lost two electrons. The ionization potential can be calculated by considering the energy difference between the initial state (Be ion with two electrons) and the final state (Be ion with one electron).

3. The initial energy level of Be ion is given by:

E_i = -13.6 eV/(2²) = -13.6 eV/4 = -3.4 eV

4. The final energy level of Be ion is given by:

E_f = -13.6 eV/(1²) = -13.6 eV

5. Substituting the values into the ionization potential formula:

Ionization Potential = E_f - E_i = -13.6 eV - (-3.4 eV) = -10.2 eV

6. The ionization potential is a positive value, so we take the absolute value:

Ionization Potential = 10.2 eV

Answer: The ionization potential of Be ion, calculated using the Bohr model, is 10.2 eV. Rounding it off to two decimal places, the correct answer is between 10.19 eV and 10.21 eV.

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