Question

4. (a) Use the Bohr model to calculate the frequency of an electron in the 149th Bohr orbit of the hydrogen atom.

(b) Find the frequency of light emitted in the transition from the 149th orbit to the 145th orbit.

Answer 1

a)
we know, radius of nth orbit, rn = 0.0529*n^2 nm

if n = 149

r = 0.0529*149^2*10^-9

= 1.174*10^-6 m

orbital speed, vn = 2.19*10^6/n

if n = 149

v = 2.19*10^6/149

= 1.47*10^4 m/s

Time prioed, T = 2*pi*r/v

frequency, f = 1/T

= v/(2*pi*r)

= 1.47*10^4/(2*pi*1.174*10^-6)

= 1.99*10^9 Hz <<<<<<<<---------Answer

b) energy of emitted photon, E = 13.6*(1/nf^2 - 1/ni^2) eV

= 13.6*(1/145^2 - 1/149^2) eV

= 3.42*10^-5 eV

we know, E = h*f

==> f = E/h

= 3.42*10^-6*1.6*10^-19/(6.626*10^-34)

= 8.26*10^8 Hz <<<<<<<<---------Answer