Finding initial and final n for hydrogen absorption at 4055 nm

[needhelpperson]

The hydrogen atom can absorb light of wavelength 4055nm. Determine the inital and final values of n associated with this absorption.

Well i figured out the Energy it absorbed

(h*c)/(wavelength)

= ((6.63*10-34)*(3*10^8))/(4055/10^9)

=4.905 * 10^-20 J

so 4905*10^-20 = -2.18*10-18*(1/nf^2 - 1/ni^2)

1/nf^2 - 1/ni^2 = -.0225

How do i solve these two unknowns, other than guess and check?

 

[K.J.Healey]

I think its pretty much guess and check from there. I get 5 and 4.

 

[needhelpperson]

I think its pretty much guess and check from there. I get 5 and 4.

ya i got the same answers... but i just wanted to see if anyone has a different method to solve this problem .