According to Bohr's theory, the moment of momentum of an electron revolving in $4^{\text {th }}$ orbit of hydrogen atom is:
Solution
<p>According to Bohr's theory, one of the postulates specifies that the angular momentum of an electron in orbit around a nucleus is quantized. This quantization can be expressed by the formula:</p>
<p>$L = n\frac{h}{2\pi}$</p>
<p>Where:</p>
<ul>
<li>$L$ is the angular momentum of the electron,</li>
<li>$n$ is the principal quantum number (or the orbit number in simpler terms), which can take positive integer values (1, 2, 3, ...),</li>
<li>$h$ is Planck's constant ($6.62607015 \times 10^{-34} m^2 kg / s$), and</li>
<li>$\frac{h}{2\pi}$ is often denoted as $\hbar$ (h-bar), known as the reduced Planck's constant.</li>
</ul>
<p>For an electron in the 4th orbit ($n = 4$) of a hydrogen atom, we substitute $n = 4$ into the equation:</p>
<p>$L = 4\frac{h}{2\pi}$</p>
<p>Therefore, the moment of momentum (or angular momentum) of an electron in the $4^{\text{th}}$ orbit of a hydrogen atom is:</p>
<p>$L = 4\frac{h}{2\pi} = 2\frac{2h}{2\pi} = 2\frac{h}{\pi}$</p>
<p>Hence, the correct option is:</p>
<p>Option A: $2 \frac{h}{\pi}$</p>
About this question
Subject: Physics · Chapter: Atoms and Nuclei · Topic: Bohr's Model of Hydrogen Atom
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