Question

Energy of electron in its nth orbit is given as

$(E_{n} = \frac{13.6}{n^{2} } \times z )ev$
consider a hydrogen atom find the amount of energy needed to transfer electron from first Orbit to third Orbit​

Answer 1

Given : Energy of electron in its nth orbit is given by, E_n = -13.6 × Z²/n² eV

To find : The amount of energy needed to transfer electron from first orbit to third orbit.

solution : for hydrogen atom, Z = 1

energy of electron in 1st orbit, E₁ = -13.6 × 1²/1² eV

= -13.6 eV

energy of electron in 3rd orbit, E₃ = -13.6 × 1²/3²

= -13.6 × 1/9 = -1.51 eV

so required energy = change in energy of electron from first orbit to 3rd orbit

= E₁ - E₃

= -13.6eV - (-1.51 eV)

= -12.09 eV

Therefore the amount of energy needed to transfer an electron from first to 3rd orbit is -12.09 eV

Answer 2

GiveN :

• $\sf{E_n\ =\ \bigg( \dfrac{-13.6}{n^2}\ \times\ z\ \bigg) \: \: \: \: eV}$

To FinD :

• Energy needed to transfer electron from first shell to third shell for hydrogen atom.

SolutioN :

$\implies \sf{E_n\ =\ \dfrac{-13.6}{n^2}\ \times\ z} \\ \\ \\ \\ \sf{Where} \: \begin{cases} \sf{z\ is\ atomic\ number} \\ \\ \sf{n\ is\ number\ of\ orbit} \end{cases}$

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$\underbrace{\sf{For\ First\ Orbit\ n\ =\ 1}} \\ \\ \\ \\ \implies \sf{E_1\ =\ \dfrac{-13.6}{1^2}\ \times\ 1} \\ \\ \\ \\ \implies \sf{E_1\ =\ \dfrac{-13.6}{1}} \\ \\ \\ \\ \implies {\underline{\boxed{\sf{E_1\ =\ -13.6\ ev}}}}$

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$\underbrace{\sf{For\ third\ orbit\ n\ =\ 3}} \\ \\ \\ \\ \implies \sf{E_3\ =\ \dfrac{-13.6}{3^2}\ \times\ 1} \\ \\ \\ \implies \sf{E_3\ =\ \dfrac{-13.6}{9}} \\ \\ \\ \\ \implies {\underline{\boxed{\sf{E_3\ =\ -1.51}}}}$

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$\underbrace{\sf{Energy\ required\ :}} \\ \\ \\ \\ \implies \sf{E\ =\ E_3\ -\ E_1} \\ \\ \\ \\ \implies \sf{E\ =\ -13.6\ -\ (-1.51)} \\ \\ \\ \\ \implies \sf{E\ =\ -13.6\ +\ 1.51} \\ \\ \\ \\ \implies {\underline{\boxed{\sf{E\ =\ -12.9\ eV}}}} \\ \\ \\ \\ \small \underline{\sf{\therefore\ Energy\ required\ is\ -12.9\ eV}}$