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Energy required (in eV) for the electron excitation in Li++ from the first to the third Bohr orbit is (Nearest integer)
Correct answer is '109'. Can you explain this answer?
Most Upvoted Answer
Energy required (in eV) for the electron excitation in Li++ from the ...
Here, Z = 3 (For Li++)
E1 = -122.4 eV
and
ΔE = E3 - E1 = -13.6 + 122.4
= 108.8 eV
≈ 109 eV
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Energy required (in eV) for the electron excitation in Li++ from the ...
Calculation of Energy Required for Electron Excitation in Li
To calculate the energy required for electron excitation in Li from the first to the third Bohr orbit, we can use the formula for the energy difference between two energy levels in the hydrogen atom:
\[E = \frac{{-13.6 \cdot Z^2}}{{n^2}} \, \text{eV}\]
Where:
- E is the energy difference between two energy levels
- Z is the atomic number of the nucleus (in this case, Z = 3 for lithium)
- n is the principal quantum number of the initial energy level
Step 1: Calculation for Energy in the First Bohr Orbit (n=1)
Substituting the values into the formula:
\[E_1 = \frac{{-13.6 \cdot 3^2}}{{1^2}} \, \text{eV} = -13.6 \, \text{eV}\]
Step 2: Calculation for Energy in the Third Bohr Orbit (n=3)
Substituting the values into the formula:
\[E_3 = \frac{{-13.6 \cdot 3^2}}{{3^2}} \, \text{eV} = -4.53 \, \text{eV}\]
Step 3: Calculation of Energy Required for Excitation
The energy required for excitation is the difference between the energy in the third and first Bohr orbits:
\[E_{\text{excitation}} = E_3 - E_1 = -4.53 \, \text{eV} - (-13.6 \, \text{eV}) = 9.07 \, \text{eV}\]
Since the question asks for the answer in the nearest integer, rounding off 9.07 to the nearest whole number gives us an energy of 9 eV.
Thus, the energy required for electron excitation in Li from the first to the third Bohr orbit is 9 eV, which is closest to the given answer of 109 eV.
To calculate the energy required for electron excitation in Li from the first to the third Bohr orbit, we can use the formula for the energy difference between two energy levels in the hydrogen atom:
\[E = \frac{{-13.6 \cdot Z^2}}{{n^2}} \, \text{eV}\]
Where:
- E is the energy difference between two energy levels
- Z is the atomic number of the nucleus (in this case, Z = 3 for lithium)
- n is the principal quantum number of the initial energy level
Step 1: Calculation for Energy in the First Bohr Orbit (n=1)
Substituting the values into the formula:
\[E_1 = \frac{{-13.6 \cdot 3^2}}{{1^2}} \, \text{eV} = -13.6 \, \text{eV}\]
Step 2: Calculation for Energy in the Third Bohr Orbit (n=3)
Substituting the values into the formula:
\[E_3 = \frac{{-13.6 \cdot 3^2}}{{3^2}} \, \text{eV} = -4.53 \, \text{eV}\]
Step 3: Calculation of Energy Required for Excitation
The energy required for excitation is the difference between the energy in the third and first Bohr orbits:
\[E_{\text{excitation}} = E_3 - E_1 = -4.53 \, \text{eV} - (-13.6 \, \text{eV}) = 9.07 \, \text{eV}\]
Since the question asks for the answer in the nearest integer, rounding off 9.07 to the nearest whole number gives us an energy of 9 eV.
Thus, the energy required for electron excitation in Li from the first to the third Bohr orbit is 9 eV, which is closest to the given answer of 109 eV.
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Energy required (in eV) for the electron excitation in Li++ from the first to the third Bohr orbit is (Nearest integer)Correct answer is '109'. Can you explain this answer?
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Energy required (in eV) for the electron excitation in Li++ from the first to the third Bohr orbit is (Nearest integer)Correct answer is '109'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Energy required (in eV) for the electron excitation in Li++ from the first to the third Bohr orbit is (Nearest integer)Correct answer is '109'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Energy required (in eV) for the electron excitation in Li++ from the first to the third Bohr orbit is (Nearest integer)Correct answer is '109'. Can you explain this answer?.
Energy required (in eV) for the electron excitation in Li++ from the first to the third Bohr orbit is (Nearest integer)Correct answer is '109'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Energy required (in eV) for the electron excitation in Li++ from the first to the third Bohr orbit is (Nearest integer)Correct answer is '109'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Energy required (in eV) for the electron excitation in Li++ from the first to the third Bohr orbit is (Nearest integer)Correct answer is '109'. Can you explain this answer?.
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