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Home » 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.
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.
CBSE | Chemistry | Class 11 | NCERT | Structure of Atom
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.

Only one electron exists in hydrogen atoms. The angular momentum of this electron, according to Bohr’s postulates, is:

m v r=n \frac{h}{2 \pi} \quad \ldots .(1)
Where, n=1,2,3, \ldots
As per de Broglie’s equation:
\lambda=\frac{h}{m v}
or m v=\frac{h}{\lambda} \quad \ldots \ldots .(2) \quad \frac{h r}{\lambda}=n \frac{h}{2 \pi}
or 2 \pi r=n \lambda \quad \ldots . .(3)

However, ‘2πr’ is the circumference of the Bohr orbit. As a result, equation (3) shows that the diameter of the Bohr orbit for the hydrogen atom is an integral multiple of the de Broglie wavelength of the electron circling around it.

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