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 = n²a_o

For n =2; r₂= (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 (9x10⁹ )/ 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