Question

Bohr and Planck's equation?

Hello,

For the following problem using Bohr and Planck's equation, which is:

`E=(hc)/λ=-R_H[1/n_i^2-1/n_f^2]`

where, `R_H=2.18*10^-18` J/electron

I set up my problem as
`E=(hc)/λ=-2.18*10^-18 [1/2_i^2-1/4_f^2]`

Since no calculators are allowed for this problem, how should I approach the fraction part step-by-step, as well as the rest of the problem to find `E`?

Thank you.

Answer 1

See below

Explanation:

If you want `E`, delete the middle bit:

`E= -2.18*10^-18 [1/2_i^2-1/4_f^2]`

You also left the subscripts in. Should read:

`E =-2.18*10^-18 [1/2 ^2-1/4 ^2]`

`=-2.18*10^-18 [3/16 ]`

You might also be better using `R approx 13.6 " eV"`

`E approx 13.6 [3/16 ]`

Then it looks pretty trivial, and the +/- sign of the answer you can verify according to common sense.

Simplifying:

• `E_n = -1/ n^2 * 13.6 " eV" , qquad n = 1,2, ...`