First slide

Quantum mechanical model of the atom

Question

If the radius of the first Bohr orbit is x, then de-Broglie wavelength of the electron in the third orbit is nearly

Moderate

A

$2 πx$
B

$6 πx$
C

9x
D

$\frac{x}{3}$

Solution

Angular momentum is quantized, hence ${mvr}_{n} \frac{nh}{2 π}$
By Bohr's theory $(a_{0} = Bohr' s radius = x)$
$r_{n} = \frac{n^{2} a_{0}}{Z} = \frac{9 a_{0}}{1} = 9 x$
$∴ mv (9 x) = \frac{3 h}{2 π}$
$∴ mv = \frac{h}{6 πx}$
By de-Broglie's equation
$λ = \frac{h}{mv} = \frac{h}{h / 6 πx} = 6 πx$

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