An electron in a hydrogen atom in its ground state absorbs energy equal to ionisation energy of `Li^(+2)`. The wavelength of the emitted electron is :-
(a). `3.32xx10^(10)m`
(b). `1.17 Å`
(c). `2.32xx10^(9)nm`
(d). `3.33"pm"`

Options

A. 3.32Ã…
B. 2.32nm
C. 1.14Ã…
D. 3.33 pm

Answer

C

Explanation

Ground state energy of hydrogen atom:
`E=-2.18xx10(-18)J`
Ionisation energy `=+(Z^(2))/(n^(2))xx2.18xx10^(-18)J`
Total energy after absorption
`=-2.18xx10^(-18)+9xx2.18xx10^(-18)`
`=8xx2.18xx10^(-18)J`
`E=(hc)/(lamda)`
`lamda=(hc)/(E)=(6.626xx10^(-34)xx3xx10^(8))/(8xx2.18xx10^(-18))`
`=1.139xx10^(-8)cm=1.14xx10^(-10)m=1.14`Ã…