De Broglie Wavelength In Bohr Orbits

De Broglie explained Bohr's quantisation by requiring that an integral number of electron wavelengths fit around each orbit, expressed as $2\pi r_n=n\lambda$. Rearranging gives the wavelength $\lambda =\frac{2\pi r_n}{n}$, which links the wave picture to the orbit geometry. For the second orbit $n=2$ and $r_2=2.12$ Å, so $\lambda =\frac{2\pi \times 2.12}{2}=\pi \times 2.12\approx 6.66$ Å. The value 3.33 Å is wrong because it forgets the factor $2\pi$ and merely halves the radius. The value 13.3 Å equals the full circumference $2\pi r_2$ and mistakenly omits dividing by $n=2$. The value 2.12 Å is simply the orbit radius and confuses radius with wavelength. This standing-wave requirement directly reproduces Bohr's angular-momentum rule $mvr=n\hslash$, showing that quantisation is a natural consequence of the electron's wave nature rather than an arbitrary postulate. This directly reflects the NCERT account of de Broglie's standing-wave condition. A plausibility check confirms two complete wavelengths ($2\times 6.66=13.3$ Å) reproduce the full orbital circumference, exactly as the $n=2$ standing-wave condition demands.