Question

# Calculate the wavelength of the photon, which excites the electron of hydrogen atom from ground state to fourth energy level. lonization energy of hydrogen atom is ( 1312 mathrm{kJ} / mathrm{mol} ).

Solution

Energy of nth orbit is given by ( mathrm{En}=-21.8 times 10^{-19} times mathrm{Z}^{2} / mathrm{n}^{2} )

If ( Z=1 ) then, ( E n=-21.8 times 10^{-19} / n^{2} ) J/atom

For fist orbit, ( mathrm{E}_{1}=-2.18 times 10^{-19} / 1^{2}=-21.8 times 10^{-19} mathrm{j} / ) atom

for 4 th orbit ( , E_{4}=-2.18 times 10^{-19} / 4^{2}=-1.36 times 10^{-19} mathrm{J} / ) atom

Now, ( Delta E=E_{4}-E_{1}=h c / lambda )

( -1.36 times 10^{-19}+2.18 times 10^{-19}=6.636 times 10^{-34} times 3 times 10^{8} / lambda )

( 2.04 times 10^{-19}=6.636 times 3 times 10^{-26} / lambda )

( lambda=97.3 mathrm{nm} )