Find out the answer to "Which transition in the hydrogen atom produces emitted..."

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Lloyd Allen

Answered question

2021-11-17

Which transition in the hydrogen atom produces emitted light with the longest wavelength?
a.

n = 4 \to n = 3,

n = 2 \to n = 1

n = 3 \to n = 2

Answer & Explanation

Kara Dillon

Beginner2021-11-18Added 12 answers

Since the smallest energy difference is inversely proportional to wavelength, it determines the longest wavelength.
Using the formula:
$\frac{1}{λ} = [\frac{1}{n_{f}^{2}} - \frac{1}{n_{i}^{2}}]$
Calculate the wavelength $(λ)$ of each electronic transition
Where in
$n = 4 \to n = 3$
$\frac{1}{λ} = [\frac{1}{3^{2}} - \frac{1}{4^{2}}]$
$λ = 20.57$
b.n=2 $\to$ n=1
$\frac{1}{λ} = [\frac{1}{1^{2}} - \frac{1}{2^{2}}]$
$λ = 1.33$
c. n= $3 \to n = 2$
$\frac{1}{λ} = [\frac{1}{2^{2}} - \frac{1}{3^{2}}]$
$λ = 7.2$
As can be seen above, a has the longest wavelength. $n = 4 \to n = 3$

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