Calculate the wavelength in Ao of the photon that is emitted when an electron in the Bohr orbit n = 2 returns to the orbit n = 1 in the hydrogen atom. The ionisation potential of the ground state of the hydrogen atom is 2.17 x 10-11 erg per atom.

λ = ?. We know that for H-atom:    En=−2.17×10−11 erg atom −n2∴  When    n=1,E1=−2.17×10−11 ergatom −12                      =−2.17×10−11 erg atom −(given) When        n=2,E2=−2.17×10−11 erg atom −22                  =−2.17×10−11 erg atom −4                   =−0.542×10−11 erg atom −∴          ΔE=E2−E1=−0.542×10−11 erg                             atom −−−2.17×10−11 erg atom-                    =1.628×10−11 erg atom −But           E=hv=hcλ.  Hence;               λ=hcE  =6.626×10−27 erg.s ×3.0×1010cms−1.628×10−11 erg atom −  =1.221×10−5cm  =1.221×10−5cm×1Ao10−8cm   =1221Ao