Q.What is the angular momentum of an electron in the 3rd orbit of an atom? OR Name the spectral series of hydrogen spectrum which lies in the visible region of the electromagnetic spectrum.

Bohr's model was designed for and works only for single-electron (hydrogen-like) systems; it breaks down once more than one electron interacts within the atom.

One key limitation of Bohr's atomic model: it successfully explains the line spectrum of hydrogen (and other hydrogen-like single-electron ions such as He$^+$, Li$^{2+}$), but it fails to explain the spectra of atoms with more than one electron, because it does not account for the electron-electron interactions/repulsions present in multi-electron atoms. (Other valid limitations include: it does not explain the relative intensities of spectral lines, the fine structure (splitting) of spectral lines, or the Zeeman/Stark effects, and it arbitr …

Bohr's third (quantisation) postulate as a formula.

Bohr's postulate of quantisation of angular momentum states that the electron can revolve only in those orbits for which its orbital angular momentum is an integral multiple of $h/2\pi$: …

Bohr's quantization condition gives $L=nh/2\pi$; for $n=3$, $L=3h/2\pi$.

According to Bohr's second postulate, the angular momentum of an electron in the $n$-th orbit is quantized: …

Bohr's angular momentum quantization gives L = nh/2π; the change from n=3 to n=1 is ΔL = 2h/2π = h/π.

By Bohr's postulate, $L_n = \dfrac{nh}{2\pi}$. For the transition from $n=3$ to $n=1$:

$\Delta L = L_3 - L_1 = \frac{3h}{2\pi} - \frac{h}{2\pi} = \frac{2h}{2\pi} = \frac{h}{\pi}$ …