Atomic Structure Result Question 10-1
10. Heat treatment of muscular pain involves radiation of wavelength of about 900 nm . Which spectral line of H -atom is suitable for this purpose? $\left[R_{\mathrm{H}}=1 \times 10^5 \mathrm{~cm}^{-1}\right.$, $\left.h=6.6 \times 10^{-34} \mathrm{Js}, c=3 \times 10^8 \mathrm{~ms}^{-1}\right]$
(2019 Main, 11 Jan I)
(a) Paschen, $5 \rightarrow 3$
(b) Paschen, $\infty \rightarrow 3$
(c) Lyman, $\infty \rightarrow 1$
(d) Balmer, $\infty \rightarrow 2$
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Answer:
Correct Answer: 10. ( b )
Solution:
$\begin{aligned} & \Delta E=h c \times \dfrac{1}{\lambda}=h c \times\left[R_{\mathrm{H}}\left(\dfrac{1}{n_1^2}-\dfrac{1}{n_2^2}\right) \times Z^2\right] \\ & \Rightarrow \dfrac{1}{n_1^2}-\dfrac{1}{n_2^2}=\dfrac{h c}{R_{\mathrm{H}} \times \lambda \times Z^2 \times h c} \quad[\text { for } \mathrm{H}, \text { atom } Z=1] \end{aligned}$
$\begin{aligned} & =\dfrac{1}{R_{\mathrm{H}} \times \lambda}=\dfrac{1}{\left(1 \times 10^7 \mathrm{~m}^{-1}\right)} \times \dfrac{1}{\left(900 \times 10^{-9} \mathrm{~m}\right)} \\ & \Rightarrow \quad \dfrac{1}{n_1^2}-\dfrac{1}{n_2^2}=\dfrac{1}{9} \\ & \end{aligned} $
So, in option (b) $\dfrac{1}{3^2}-\dfrac{1}{\infty^2}=\dfrac{1}{9}-0=\dfrac{1}{9} \quad\left[\begin{array}{l}\therefore n_1=3, \\ n_2=\infty\end{array}\right]$
BETA
