13.6 text{ eV} energy is required to separate | vedclass

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(D) For a hydrogen atom in the ground state $(n=1)$,Bohr's quantization condition for angular momentum is given by $mvr = \frac{nh}{2\pi}$.Here,$m$ is

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$2.2 	imes 10^6 	ext{ ms}^{-1}$

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(D) For a hydrogen atom in the ground state $(n=1)$,Bohr's quantization condition for angular momentum is given by $mvr = \frac{nh}{2\pi}$.Here,$m$ is the mass of the electron $(9.1 	imes 10^{-31} 	ext{ kg})$,$v$ is the velocity,$r$ is the orbital radius $(5.3 	imes 10^{-11} 	ext{ m})$,and $h$ is Planck's constant $(6.63 	imes 10^{-34} 	ext{ Js})$.Rearranging the formula for velocity $v$,we get $v = \frac{h}{2\pi mr}$.Substituting the values: $v = \frac{6.63 	imes 10^{-34}}{2 	imes 3.14159 	imes 9.1 	imes 10^{-31} 	imes 5.3 	imes 10^{-11}}$.Calculating this,$v \approx 2.18 	imes 10^6 	ext{ ms}^{-1}$.Rounding to two significant figures,we get $v \approx 2.2 	imes 10^6 	ext{ ms}^{-1}$.

$13.6 \text{ eV}$ energy is required to separate a hydrogen atom into a proton and an electron. If the orbital radius of an electron in a hydrogen atom is $5.3 \times 10^{-11} \text{ m}$,then the velocity of the electron is . . . . . . .

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