The electron energy in hydrogen atom is given by `E_(n) = (-21.7 xx 10^(-12)/(n^(2))) erg`. Calculate the energy required to remove an electron completely from the `n = 2` orbit.What is the longest wavelength (in cm) of light can be used to cause this transition ?

Explanation

The energy required to remove an electron from the second orbit is the same as the energy released `(Delta E)` when an electron will drop from the infinite orbit to the second orbit. Thus, `Delta E= -(21.7 xx 10^(-12))/(oo^(2))- (-(21.7 xx 10^(-12))/(2^(2)))`
`=0+ (21.7 xx 10^(-12))/(2^(2))= 5.42 xx 10^(-12)` erg
Now we know `DeltaE = hv = (hc)/(lamda)`
`therefore (hc)/(lamda)=5.42 xx 10^(-12)`
`lamda= (6.62 xx 10^(-27) xx 3 xx 10^(10))/(5.42 xx 10^(-12))=3.66 xx 10^(-5)cm`