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

Answer:

(c) 6.91x10^14 Hz

Explanation:

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

$E = -E_0/n^2$

where  $E_0=13.6eV$

$E_2 =\frac{-13.6}{2^2}=-3.4eV$

$E_5 =\frac{-13.6}{5^2}=-0.544eV$

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 ($c=3 \times10^8m/s$) and $h$ is Planck's constant ($h=4.14\times10^{-15}eVs$). Solve for $\lambda$:

$E = hc/\lambda\\\lambda E = hc\\\lambda = \frac{hc}{E} \\\lambda = \frac{(4.14\times10^{-15})(3 \times10^8)}{2.856}=4.35\times10^{-7}m$

The frequency of this wavelength is calculated with this formula:

$f=\frac{c}{\lambda}$

$f=\frac{3\times10^8}{4.3487\times10^{-7}} =6.89\times10^{14}Hz\approx6.9\times10^{14}Hz$