Question

With some manipulation, the Rydberg equation can be rewritten in the form E=constant×(1nf2−1ni2) which allows you to calculate the energy of the emitted light. What is the value of the constant needed to complete this equation?

Answer 1

E= constant * (1/nf^2- 1/ni^2)

You have to find the relation between Ryhbergs equation and the energy equation in order to find the constant in the above equation, so we have to find the relation between wavelength and frequency and energy, here are the equation to find the relation:

thus,

c= wavelength (T) x frequency(v)
so we can find frequency (v)

v=c/T

E=hv thus we can say, E= hc/T because v =c/T
so frequency (v)= E/h

so now we can make a connection between c=Tv and E=hv

C= TE/h
recall that C = T x v and frequency(v) = E\h which we found beforehand.

no we solve for wavelength(T) :
which equals :
(T)=ch/E
then find the inverse of wavelength since that is what is used in rybergs equation.

1/T= E/ch

then to relate it to rybergs equation which is
E= constant * (1/nf^2- 1/ni^2) we combine them which results in


E/ch= RH(1/nf^2- 1/ni^2)
rearramged to find constant:
E= RHch (1/nf^2- 1/ni^2)

recall the values of:
h=6.626x10^-34
c=2.998x10^8
RH= 1.097x10^7

thus you multiply all values and you get 2.18x10^-18J for the constant