The de-Broglie wavelength associated with the | vedclass

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(B) The de-Broglie wavelength $\lambda$ of an electron is given by $\lambda = \frac{h}{mv}$.According to Bohr's theory,the velocity $v$ of an electron

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four times the de-Broglie wavelength of the electron in the ground state

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(B) The de-Broglie wavelength $\lambda$ of an electron is given by $\lambda = \frac{h}{mv}$.According to Bohr's theory,the velocity $v$ of an electron in the $n^{th}$ orbit is inversely proportional to the principal quantum number $n$,i.e.,$v \propto \frac{1}{n}$.Substituting this into the wavelength formula,we get $\lambda = \frac{h}{m(k/n)} = \frac{h}{mk} \cdot n$,which implies $\lambda \propto n$.For the ground state $(n = 1)$,let the wavelength be $\lambda_1$.For the $n = 4$ level,the wavelength $\lambda_4$ is given by $\lambda_4 = 4 \lambda_1$.Therefore,the de-Broglie wavelength in the $n = 4$ level is four times the de-Broglie wavelength in the ground state.

The de-Broglie wavelength associated with the electron in the $n = 4$ level is

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