Question

Find the wavelengths in a hydrogen spectrum between the range $500nm$ to $700nm$.

• A. $540nm$
• B. $280nm$
• C. $656nm$
• D. $696nm$

Answer 1

The correct option is C $656nm$

Apply Rydberg formula.

Rydberg formula,

$\frac{1}{\lambda }=R{Z}^2(\frac{1}{n^{\prime 2}}-\frac{1}{n^2})$

Balmer series, $(z=1,n^{\prime }=2,n=3,4,5,6)$

$R=1.09737\times {10}^{-7}{m}^{-1}$

$\lambda =\frac{1}{R{Z}^2(\frac{1}{n^{\prime 2}}-\frac{1}{n^2})}=\frac{1}{(1.09737\times {10}^{-7})\times 1^2(\frac{1}{2^2}-\frac{1}{n^2})}$

For $n=3,4,5,\mathrm{6...}$ $656.11nm,486nm,433nm,410nm\dots$

Hence, $656.11nm$ is the correct answer.