What is the wavelength of light emitted

Solution:

The ni = 4 to nf = 2 transition will give rise to a spectral line of the Balmer series. The energy involved in the transition is given by the relation,

$E=2.18 \times 10^{-18}\left[\frac{1}{n_{i}^{2}}-\frac{1}{n_{j}^{2}}\right]$

Substituting the values in the given expression of E

$E=2.18 \times 10^{-18}\left[\frac{1}{4^{2}}-\frac{1}{2^{2}}\right]$

$=2.18 \times 10^{-18}\left[\frac{1-4}{16}\right]$

$=2.18 \times 10^{-18} \times\left(-\frac{3}{16}\right)$

$\left.E=-\left(4.0875 \times 10^{-19}\right]\right)$

$\left.E=-\left(4.0875 \times 10^{-19}\right]\right)$

Wavelength of light emitted $\quad(\lambda)=\frac{\text { hc }}{E}$

$\left(\right.$ since $\left.E=\frac{h c}{\lambda}\right)$

Substituting the values in the given expression of $\lambda:$