Question

Use the Rydberg equation to calculate the wavelength (in Å) of the photon absorbed when a hydrogen atom undergoes a transition from n = 1 to n = 3.

Answer 1

Answer:

1024Å

Explanation:

The Rydberg equation is an empirical relationship equation expressed by Balmer and Rydberg which is given as:

1/λ = $R_{H} (\frac{1}{n_{f} ^{2} }-\frac{1}{n_{i} ^{2} } )$.............................(1)

where $R_{H}$ is the Rydberg constant given as $1.09 x 10^{7}m^{-1}$, n is the transition level and the subscript f and i show the final and initial level numbers respectively. λ is the wavelength.

$n_{f}$= 1

$n_{i} = 3$

Using equation (1), we have

1/λ $= 1.097 x 10^{7}(\frac{1}{3^{2} }- \frac{1}{1^{2} })$

    = $1.097 x 10^{7} (\frac{1}{9} -\frac{1}{1} )$

      = $1.097 x 10^{7}(0.11-1)$

       = $1.097 x 10^{7} (-0.89)$

       = - 9763300

λ = $-\frac{1}{9763300}$

   = $-1.024x 10^{-7}m$

We should note that the negative sign we have is as a result of photon absorption whereby the hydrogen atom gains energy to undergo a transition from the lower energy level to a higher one. Wavelength does not have a negative value.

To convert to Å, we have

λ = $\frac{1.024 x 10^{-7} }{10^{-10} }$ = 1024Å  

Therefore the wavelength of the photon in Å  is 1024Å