Question

What is the wavelength of light for the least energetic photon emitted in the Lyman series of the hydrogen spectrum. (take $hc=1240eVnm$)

• A. $82nm$
• B. $102nm$
• C. $122nm$
• D. $150nm$

Answer 1

The correct option is C $122nm$

Least energetic photon in Lyman series is emitted when an electronic transition takes place from $n=2$ to $n=1$.

Wavelength of light for least energetic photon emitted in Lyman series of hydrogen atom

$\frac{1}{\lambda }=R(\frac{1}{n_2^2}-\frac{1}{n_1^2})$ where $n_1=2$ and $n_2=1$, $R=0.010972$ $n{m}^{-1}$

$\therefore$ $\frac{1}{\lambda }=0.010972(\frac{1}{1}-\frac{1}{2^2})$ $⟹\lambda =122$ nm