Question

The energy of a hydrogen atom is -3.40 eV. What is the electrons kinetic energy?

Please write out what equation you used.

Answer #1

Incoming electron have kinetic energy KE = ΔE = 3.4 eV

( No need to use any other formula )

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If you go with calculations,

E = ( -13.6 / n^2 ) eV = -3.40 eV

On simplifying, principle quantum number, n = 2

Now, find radius of second orbit, using the formula,

r_{n} = n^{2}a_{o}

For n =2; r_{2}= (2)^{2} ( 0.529 nm ) = 0.212
nm

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Kinetic energy of electron,

KE = Ze^2 / 2 (4πεo ) r_{n}

On substituting numericals

KE = (1) (1.6 x 10^{-19} C )^{2}
(9x10^{9} )/ 2 ( 0.212x10^{-9} m )

= 3.40 ( 1.6 x10^{-19} ) V

As charge of electron is represented as e = 1.6
x10^{-19} C

In terms of electon volts, KE = 3.40 eV

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