Which of the following electron transitions in a hydrogen atom

Asked by admin @ 05/08/2021 in Chemistry viewed by 291 People

which of the following electron transitions in a hydrogen atom will require the largest amount of energy?(1)from n=1 to n=2 (2) from n=2 to n=3 (3)from n=infinite to n=1 (4) from n=3 to n= 5

Answered by admin @ 05/08/2021

Answer: The correct option is 1.

Explanation: Energy associated to the ground state energy level for H-atom: $E_o=-13.6 eV$

Energy associated to the $n^{th}-level$ for H-atom = $\frac{-E_o\times Z^2}{n^2}=\frac{-E_o}{n^2}$ (Z for H-atom = 1)

Energy difference is calculated by:

$\Delta E=E_{final}-E_{initial}$

For option 1:

$\Delta E=E_2-E_1$

$\Delta E=\frac{-13.6}{4}-\frac{-13.6}{1}=10.2eV$

For option 2:

$\Delta E=E_3-E_2$

$\Delta E=\frac{-13.6}{9}-\frac{-13.6}{4}=1.89eV$

For option 3:

$\Delta E=E_{1}-E_{\infty }$

$\Delta E=\frac{-13.6}{1}-\frac{-13.6}{\infty }=-13.6eV$

For option 4:

$\Delta E=E_{5}-E_3$

$\Delta E=\frac{-13.6}{25 }-\frac{-13.6}{9}=0.967eV$

From the above calculations, it is seen that the largest amount of energy will be required for the the transition from n= 1 to n = 2.

Hence, the correct option is 1.

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