Question

Sorry to make you use the calculator so much, but what is the frequency range of the Paschen series? This practice will help you remember the Rydberg relation for line spectra permanently, I promise. (1 THz=〖10〗^12 Hz.)

• A. 285−365 THz
• B. 820−1875 THz
• C. 160−366 THz
• D. 490−783 THz

Answer 1

The correct option is C 160−366 THz

Lyman…1, Balmer…2, Paschen! So, $n_1=3and{n}_2$ will go from $n_2=4to{n}_2=\infty$

Let ${\lambda }_1$ be the wavelength for $n_2=4,and{\lambda }_{\infty }$ for $n_2=\infty$. From the Rydberg formula,
$\frac{1}{{\lambda }_1}=R(\frac{1}{3^2}-\frac{1}{4^2})$
$\Rightarrow {\lambda }_1=1.875\times {10}^{-6}m$
$\Rightarrow v_1=\frac{c}{{\lambda }_1}=\frac{3\times {10}^8}{1.875\times {10}^{-6}}Hz=1.600\times {10}^{14}Hz$
Similarly, for $n_2=\infty$
$\frac{c}{{\lambda }_{\infty }}=R(\frac{1}{3^2}-\frac{1}{{\infty }^2})=\frac{R}{9}{m}^{-1}$
$\Rightarrow {\lambda }_{\infty }=\frac{9}{R}m=8.204\times {10}^{-7}m$
$v_{\infty }=\frac{c}{{\lambda }_{\infty }}=\frac{3\times {10}^8}{8.204\times {10}^{-}7}Hz=3.657\times {10}^{14}Hz$
${10}^{12}$ Hz makes 1 Tera Hz or 1 Thz. The frequency range $v_1–v_{\infty }$ of the Balmer series is therefore 160.0 – 365.7 THz.