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Predict which of the following statement...

Predict which of the following statements are true or false.
It takes less energy to ionize (or remove) an electron from first excited state than the ground state of H-atom.

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To determine whether the statement "It takes less energy to ionize (or remove) an electron from the first excited state than the ground state of H-atom" is true or false, we can analyze the ionization energies from both states using the Bohr model of the hydrogen atom. ### Step-by-Step Solution: 1. **Understanding Ionization Energy**: - Ionization energy is the energy required to remove an electron from an atom. For the hydrogen atom, we can calculate the ionization energy from different energy levels. 2. **Bohr's Model Energy Formula**: - According to Bohr's model, the energy of an electron in the n-th orbit is given by the formula: \[ E_n = -\frac{13.6 \, Z^2}{n^2} \text{ eV} \] - For hydrogen (Z = 1), this simplifies to: \[ E_n = -\frac{13.6}{n^2} \text{ eV} \] 3. **Calculating Ionization Energy from the Ground State (n=1)**: - For the ground state (n=1): \[ E_1 = -\frac{13.6}{1^2} = -13.6 \text{ eV} \] - The ionization energy from the ground state to infinity (E_infinity = 0) is: \[ \text{Ionization Energy from Ground State} = E_{\infty} - E_1 = 0 - (-13.6) = 13.6 \text{ eV} \] 4. **Calculating Ionization Energy from the First Excited State (n=2)**: - For the first excited state (n=2): \[ E_2 = -\frac{13.6}{2^2} = -\frac{13.6}{4} = -3.4 \text{ eV} \] - The ionization energy from the first excited state to infinity is: \[ \text{Ionization Energy from First Excited State} = E_{\infty} - E_2 = 0 - (-3.4) = 3.4 \text{ eV} \] 5. **Comparing Ionization Energies**: - From the calculations: - Ionization energy from the ground state = 13.6 eV - Ionization energy from the first excited state = 3.4 eV - Since 3.4 eV < 13.6 eV, it takes less energy to ionize an electron from the first excited state than from the ground state. 6. **Conclusion**: - Therefore, the statement "It takes less energy to ionize (or remove) an electron from the first excited state than the ground state of H-atom" is **True**.
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