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  • Calculate the principal quantum number of the hydrogen atom when its radius after collision with an electron was found to be <img alt="47.7 \times 10^{-11} \mathrm{~m}" src="https://entrancecorner.

Calculate the principal quantum number of the hydrogen atom when its radius after collision with an electron was found to be 47.7 \times 10^{-11} \mathrm{~m}. Also, in the fist excited state its radius was found to be 21.2 \times 10^{-11} \mathrm{~m}.

Option: 1

\mathrm{n=4}


Option: 2

\mathrm{n=2}


Option: 3

\mathrm{n=16}


Option: 4

\mathrm{n=3}


Answers (1)

best_answer

\mathrm{r\, \alpha \, n^2}

\mathrm{\frac{r_f}{r_i}=\left(\frac{n_f}{n_i}\right)^2}

\mathrm{\frac{47.7 \times 10^{-11}}{21.2 \times 10^{-11}}=\left(\frac{n_f}{2}\right)^2 }

\mathrm{n^2=9 }

\mathrm{n= 3}

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