Question

An excited hydrogen atom emits light with a wavelength of 397.2 nm to reach the
energy level for which n = 2. In which principal quantum level did the electron
begin? (c = 3.00 x 108 m/s, h = 6.63 x 10-34 J•s, RH = 2.18 x 10-18J).

Answer 1

According to Rydberg equation

= R_H × ( - ₎

given, = 397.2 nm = 397.2 ×10^-9 m .

n_i = 2

R_H = 2.18×10^-18 J = ( 2.18×10^-18 × ) m^-1

= 2.18×10^-18 × m^-1

= 1.096 ×10⁷ m^-1 .

so,

= 1.096 × 10⁷ ( - )

or, ( - ) =

or, = ( - 0.2296 )

or, = 0.0205

or, n_f² = 49

or, n_f = 7.

Hence, the electron began at principal quantum number 7.