Discussion Forum

A hydrogen atom is an exciting state of principal quantum number (n), it emits a photon of wavelength ($\lambda$). when it returns to the ground state. the value of n is 

Answer:

Explanation:

As   $\frac{1}{\lambda}= R\left(\frac{1}{n^{2}_{1}}-\frac{1}{n^{2}_{2}}\right)$

 $\therefore$    $\frac{1}{\lambda}= R\left(\frac{1}{1^{2}}-\frac{1}{n^{2}_{}}\right)$

 Mutliply both sides by $\lambda$

 $1= \lambda R\left(1-\frac{1}{n^{2}_{}}\right)or \frac{1}{\lambda R}= 1-\frac{1}{n^{2}}$

 or   $ \frac{1}{n^{2}}=1-\frac{1}{\lambda R}=\frac{\lambda R-1}{\lambda R}$

   or    $n= \sqrt{\frac{\lambda R}{\lambda R-1}}$