QJEEM24Ph3d1a: JEE Main 2024 Physics - Class 12 JEEM24Ph3d1a Solution: According to Bohr's theory, the moment of momentum of an…

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:

$$L=n\frac{h}{2\pi }$$

Where:

• $L$ is the angular momentum of the electron,
• $n$ is the principal quantum number (or the orbit number in simpler terms), which can take positive integer values (1, 2, 3, ...),
• $h$ is Planck's constant ( $6.62607015 \times 10^{-34} m^2 kg / s$ ), and
• $\frac{h}{2\pi}$ is often denoted as $\hbar$ (h-bar), known as the reduced Planck's constant.

For an electron in the 4th orbit ( $n = 4$ ) of a hydrogen atom, we substitute $n = 4$ into the equation:

$$L=4\frac{h}{2\pi }$$

Therefore, the moment of momentum (or angular momentum) of an electron in the $4^{\text{th}}$ orbit of a hydrogen atom is:

$$L=4\frac{h}{2\pi }=2\frac{2h}{2\pi }=2\frac{h}{\pi }$$

Hence, the correct option is:

Option A: $2 \frac{h}{\pi}$