Speed of electron in its 1^{st} Bohr's orbit | vedclass

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(C) Given,speed of the electron in $1^{st}$ Bohr's orbit,$v_1 = 2.18 	imes 10^6 \ m/s$. Time period of $n^{th}$ orbit,$T_n = 4.10 \ fs = 4.10 	imes

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$3$

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(C) Given,speed of the electron in $1^{st}$ Bohr's orbit,$v_1 = 2.18 	imes 10^6 \ m/s$. Time period of $n^{th}$ orbit,$T_n = 4.10 \ fs = 4.10 	imes 10^{-15} \ s$. Radius of Bohr's first orbit,$r_1 = 0.53 	imes 10^{-10} \ m$. Orbital period of electron in Bohr's first orbit is $T_1 = \frac{2 \pi r_1}{v_1} = \frac{2 	imes 3.14 	imes 0.53 	imes 10^{-10}}{2.18 	imes 10^6} \approx 1.52 	imes 10^{-16} \ s$. The time period of the $n^{th}$ orbit is related to the first orbit by $T_n = n^3 T_1$. Therefore,$n^3 = \frac{T_n}{T_1} = \frac{4.10 	imes 10^{-15}}{1.52 	imes 10^{-16}} \approx 26.97 \approx 27$. Thus,$n = (27)^{1/3} = 3$.

Speed of electron in its $1^{st}$ Bohr's orbit is given by $2.18 \times 10^6 \ m/s$. If the time period of electron in $n^{th}$ orbit is measured as $4.10 \ fs$,the value of $n$ is

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