Angular momentum of an electron in a hydrogen atom is 3h/π, then the energy of the electron is _______ eV.

The correct answer is Option 3. Full mathematical solution steps and hints are accessible in the interactive StemCET workspace.

Physics Q44 – JEE-MAIN 2026

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Home Physics Structure of AtomQuestion #481

Angular momentum of an electron in a hydrogen atom is

\frac{3 h}{π}

, then the energy of the electron is _______ eV.

Clue 1 of 3: Bohr's Model Quantization

Recall the quantization condition for angular momentum in Bohr's model of the hydrogen atom.

🧠 Full Solution Path

Step 1: Determine the principal quantum number (n)✦ Active

The angular momentum of an electron in a hydrogen atom is given by Bohr's quantization rule as $L = n \frac{h}{2 π}$ , where $n$ is the principal quantum number and $h$ is Planck's constant.

We are given that the angular momentum $L = \frac{3 h}{π}$ .

n \frac{h}{2 π} = \frac{3 h}{π}

Solving for $n$ :

n = \frac{3 h}{π} \times \frac{2 π}{h} = 6

Step 2: Calculate the energy of the electron○ Expand

The energy of an electron in the $n$ -th orbit of a hydrogen atom is given by the formula:

E_{n} = - \frac{13.6}{n^{2}} eV

Substitute the value of $n = 6$ into the energy formula:

E_{6} = - \frac{13.6}{6^{2}} = - \frac{13.6}{36}

Calculating the value:

E_{6} \approx - 0.3777 . . . eV

Rounding to two decimal places, $E_{6} \approx - 0.38$ eV.

Step 3: Match the result with the given options○ Expand

The calculated energy of the electron is approximately $- 0.38$ eV, which matches option 3.

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Physics Question 44 – JEE-MAIN 2026

Clue 1 of 3: Bohr's Model Quantization

🧠 Full Solution Path