Question

what frequency of light must an electron in hydrogen absorb to jump from the n=2 state to the n=5 state? (a) 2.86 Hz (b) 4.08 Hz (c) 6.91x10^14 Hz (d) 9.86x10^14 Hz

Answer 1

(c) 6.91x10^14 Hz

Step-by-step explanation:

Find the level energy of n=2 and n=5, using the formula:

`E = -E_0/n^2`

where
`E_0=13.6eV`

`E_2 =(-13.6)/(2^2)=-3.4eV`

`E_5 =(-13.6)/(5^2)=-0.544eV`

To jump from n=2 to n=5 the electron absorbs a photon with energy equal to
`(-0.544) - (-3.4)=2.856eV`, using the next formula to find specific wavelength
`\lambda` to that energy

`E = hc/\lambda`

Where
`c` is the speed of light (
`c=3 *10^8m/s`) and
`h` is Planck's constant (
`h=4.14*10^(-15)eVs`). Solve for
`\lambda`:

`E = hc/\lambda\\\lambda E = hc\\\lambda = (hc)/(E) \\\lambda = ((4.14*10^(-15))(3 *10^8))/(2.856)=4.35*10^(-7)m`

The frequency of this wavelength is calculated with this formula:

`f=(c)/(\lambda)`

`f=(3*10^8)/(4.3487*10^(-7)) =6.89*10^(14)Hz\approx6.9*10^(14)Hz`