Question

an electron in a hydrogen atom in its ground state absorbs twice its ionisation energy .What is the wavelength of the emitted electron?

Answer 1

we know,
according to Einstein theory ,
Kinetic energy = energy supplied - energy require to remove electrons ( I.E)

A/C to question ,
energy supplied = 2 × I.E
so,
K.E = 2× I.E - I.E = I.E

e.g kinentic energy = I.E
but we know ,
I.E = 13.6 × Z²/n² eV
where , Z is atomic number and n is orbit number
here , Z = 1 and n = 1
I.E = 13.6 ev

so, K.E = 13.6 ev

now, use concept De-broglie theory
wavelength = planks constant/√(2m.K.E)

K.E = 13.6 × 1.6× 10^-19 j
m = 9.1 × 10^-31 kg
h = 6.626 × 10^-34 j.s

so, wavelength = 6.626×10^-34 /√{2 ×9.1×10^-31 × 13.6×1.6×10^-19 } m

= 6.626× 10^(-34+25)/19.9 m

= 66.26 × 10^-10/19.9 m

= 3.32 × 10^-10 m

= 3.32 A°

Answer 2

answer is 3.33 *10^-10 m