(solved)Question 2.13 of NCERT Class XI Chemistry Chapter 2

What is the wavelength of light emitted when the electron in a hydrogen atom undergoes transition from an energy level with n = 4 to an energy level with n = 2?
(Rev. 20-Nov-2022)

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Question 2.13NCERT Class XI Chemistry

What is the wavelength of light emitted when the electron in a hydrogen atom undergoes transition from an energy level with n = 4 to an energy level with n = 2?

Video Explanation(detailed solution given after this video)

Please watch this youtube video for a quick explanation of the solution:

Solution in Detail

Given $\displaystyle n_i = 4\text{, } n_f = 2$

visible Balmer emission because $\displaystyle n_f = 2$

Calculate wave number first:

$\displaystyle \overline{\nu} = 1.09677 \times 10^7 \bigg(\frac{1}{n_i^2} - \frac{1}{n_f^2}\bigg)\text{(/m)}$

$\displaystyle = 1.09677 \times 10^7 \bigg(\frac{1}{4^2} - \frac{1}{2^2}\bigg) \text{(/m)}$

$\displaystyle = -2.06 \times 10^6 \text{ /m}$

-ve sign means emission. can be ignored.

but wavelength $\displaystyle \lambda = \frac{1}{\overline{\nu} }$

$\displaystyle = \frac{1}{2.06 \times 10^6 } \text{ m}$

$\displaystyle = 486 \times 10^{-9} \text{ m} = 486 \text{ nm }\underline{Ans}$