Show that the circumference of the Bohr ...

NCERT Class XI Chemistry Structure of Atom Solutions

Question : 32 of 67

Marks: +1, -0

Show that the circumference of the Bohr orbit for the hydrogen atom is an integral multiple of the de Broglie wavelength associated with the electron revolving around the orbit.

Solution:

According to Bohr’s theory, the angular momentum of an electron of mass (m) moving with speed (v) in an orbit of radius (r) is an integral multiple of

\frac{h}{2\pi}

mvr =

\frac{nh}{2\pi}

or 2πr =

\frac{nh}{mv}

... (1)

But according to de Broglie equation, λ =

\frac{h}{mv}

... (2)

From equations (1) and (2), we get 2πr = nλ, i.e., an integral multiple of the de Broglie wavelength.

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