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  4. If the de-Broglie wavelength of the fourth Bohr orbit of hydrogen atom is 4 overset texto mathop textA , the circumference of the orbit will be

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Q. If the de-Broglie wavelength of the fourth Bohr orbit of hydrogen atom is $ 4\overset{\text{o}}{\mathop{\text{A}}}\, $ , the circumference of the orbit will be

Rajasthan PMTRajasthan PMT 2011

Solution:

According to Bohrs postulate and de-Broglie equation $ 2\pi r=n\lambda $ Here, $ 2\pi r= $ circumference of the orbit $ n=4 $ $ \lambda =4\overset{\text{o}}{\mathop{\text{A}}}\, $ $ \therefore $ $ 2\pi r=4\times 4 $ $ =16\overset{\text{o}}{\mathop{\text{A}}}\, $