A 12.5 eV electron beam is used to bombard gaseous hydrogen at room temperature. Upto which energy. Level the hydrogen atoms would be excited ? Calculate the wavelengths of the first memeber of Lyman and first member of Balmer series.

Explanation

Here, `DeltaE`= 12.5 eV
Energy of an electron in the nth orbit of hydrogen atom is `En = -13.6/n^2`eV
For ground state n = 1,
`E_1=-13.6/1^2eV=-13.6` eV
For first excited state n = 2,
`E_2=-(13.6)/2^2`eV=-3.4 eV
For second excited state n = 3,
`E_3=-13.6/3^2`eV=-1.51 eV
Energy required to excite hydrogen atoms from ground state to the second excited state
`=E_("final")-E_("initial")`
= –151 –(–13.6) = 12.09 eV
Thus hydrogen atoms would be excited upto third energy level (n = 3).
For Lyman series,
`1/lambda=R(1/(n^2f)-2/(n_i^2))`
`1/lambda=1.097xx10^7(1/1^2-1/2^2)`
`1/lambda=1.097xx10^7xx3/4`
`1/lambda=0.82275xx=10^7 m^(-1)`
`lambda=122xx10^(-9)`m =122 nm
For Balmer series
`1/lambda=1.097xx10^7(1/2^2-1/3^3)`
`1/lambda=1.097xx10^7xx5/36`
`1/lambda=0.15236xx10^7`
`lambda`=656.3 nm