The de-Broglie wavelength of the electron in | vedclass

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(B) According to the de-Broglie hypothesis,a revolving electron in a circular orbit exhibits wave nature.For a stable circular orbit,the circumference

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equal to the circumference of the first orbit

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(B) According to the de-Broglie hypothesis,a revolving electron in a circular orbit exhibits wave nature.For a stable circular orbit,the circumference of the orbit must be an integral multiple of the de-Broglie wavelength,which is given by the condition:$2 \pi r_n = n \lambda$where $r_n$ is the radius of the $n$th orbit,$n$ is the principal quantum number,and $\lambda$ is the de-Broglie wavelength.For the first Bohr orbit,$n = 1$.Substituting $n = 1$ into the equation,we get:$2 \pi r_1 = 1 \cdot \lambda$$\lambda = 2 \pi r_1$Thus,the de-Broglie wavelength of the electron in the first Bohr orbit is equal to the circumference of the first orbit.

The de-Broglie wavelength of the electron in the first Bohr orbit of the hydrogen atom is

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