JEE MAIN - Chemistry (2023 - 24th January Morning Shift - No. 23)
If wavelength of the first line of the Paschen series of hydrogen atom is 720 nm, then the wavelength of the second line of this series is _________ nm. (Nearest integer)
Answer
492
Explanation
$\frac{1}{720}=R \times\left(\frac{1}{9}-\frac{1}{16}\right)$
$$ \begin{aligned} & \Rightarrow R=\frac{9 \times 16}{720 \times 7} \\\\ & \frac{1}{\lambda^{\prime}}=\frac{9 \times 16}{720 \times 7} \times\left(\frac{1}{9}-\frac{1}{25}\right) \\\\ & \lambda^{\prime}=492.18 \mathrm{~nm} \\\\ & \lambda^{\prime}=492 \mathrm{~nm} \text { (nearest integer) } \end{aligned} $$
$$ \begin{aligned} & \Rightarrow R=\frac{9 \times 16}{720 \times 7} \\\\ & \frac{1}{\lambda^{\prime}}=\frac{9 \times 16}{720 \times 7} \times\left(\frac{1}{9}-\frac{1}{25}\right) \\\\ & \lambda^{\prime}=492.18 \mathrm{~nm} \\\\ & \lambda^{\prime}=492 \mathrm{~nm} \text { (nearest integer) } \end{aligned} $$
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