KCET · Physics · Dual Nature of Matter
Total energy of electron in an excited state of hydrogen atom is \( -3.4 \mathrm{eV} \). The kinetic and
potential energy of electron in this state
- A \( \mathrm{K}=-3.4 \mathrm{eV} \quad U=-6.8 \mathrm{eV} \)
- B \( \mathrm{K}=3.4 \mathrm{eV} \quad \mathrm{U}=-6.8 \mathrm{eV} \)
- C \( \mathrm{K}=-6.8 \mathrm{eV} \quad U=+3.4 \mathrm{eV} \)
- D \( \mathrm{K}=+10.2 \mathrm{eV} \quad \mathrm{U}=-13.6 \mathrm{eV} \)
Answer & Solution
Correct Answer
(B) \( \mathrm{K}=3.4 \mathrm{eV} \quad \mathrm{U}=-6.8 \mathrm{eV} \)
Step-by-step Solution
Detailed explanation
Given, total energy of electron \(=-3.4 \mathrm{eV}\)
Now, \(\mid\) total energy \(|=|\) kinetic energy \(\mid\)
Therefore, kinetic energy of electron in this excited state is \(3.4 \mathrm{eV}\)
Potential energy of electron \(=2 \times\) Total energy
\(=2 \times(-3.4 \mathrm{eV})=-6.8 \mathrm{eV}\)
\((\because\) Total energy = Kinetic energy + Potential energy \(\Rightarrow 2 \times\) Total energy = Potential energy )
Therefore, kinetic energy and potential energy of electron in this state is \(3.4 \mathrm{eV}\) and \(-6.8 \mathrm{eV}\), respectively
Now, \(\mid\) total energy \(|=|\) kinetic energy \(\mid\)
Therefore, kinetic energy of electron in this excited state is \(3.4 \mathrm{eV}\)
Potential energy of electron \(=2 \times\) Total energy
\(=2 \times(-3.4 \mathrm{eV})=-6.8 \mathrm{eV}\)
\((\because\) Total energy = Kinetic energy + Potential energy \(\Rightarrow 2 \times\) Total energy = Potential energy )
Therefore, kinetic energy and potential energy of electron in this state is \(3.4 \mathrm{eV}\) and \(-6.8 \mathrm{eV}\), respectively
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