Question 523: Atoms & Nuclei

Question

If the speed of an electron of hydrogen atom in the ground state is $2.2 	imes 10^6 \mathrm{~m} / \mathrm{s}$, then its speed in the third excited state will be

Accepted Answer

Speed of electron of hydrogen atom in ground state,
$$\begin{aligned}
& v_1=22 	imes 10^6 \mathrm{~m} / \mathrm{s} \
& 	ext { Since, } \quad v \propto \frac{1}{n} \
& 	herefore \quad \frac{v_1}{v_2}=\frac{n_2}{n_1}=\frac{2.2 	imes 10^6}{v_2} \
& 	ext { [for third excited state, } n_2=4 	ext { ] } \
& \Rightarrow \quad v_2=\frac{2.2 	imes 10^6}{4}=0.55 	imes 10^6 \mathrm{~m} / \mathrm{s} \
& =5.5 	imes 10^5 \mathrm{~m} / \mathrm{s}
\end{aligned}$$

Answer

$5.5 	imes 10^6 \mathrm{~m} / \mathrm{s}$

Answer

$5.5 	imes 10^5 \mathrm{~m} / \mathrm{s}$

Answer

$8.8 	imes 10^5 \mathrm{~m} / \mathrm{s}$

Answer

$6.8 	imes 10^6 \mathrm{~m} / \mathrm{s}$

Atoms & Nuclei

If the speed of an electron of hydrogen atom in the ground state is 2.2 \times 10^6 \mathrm{~m} / \mathrm{s}, then its speed in the third excited state will be

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