Question

The wavelength of first line of lyman series in hydrogen tom is 1216 angstrom. the wavelength of first line of lyman series for 10 times ionsied sodium atom will be

• A. 0.1 angstrom
• B. 1000 angstrom
• C. 100 angstrom
• D. 10 angstrom

Answer 1

The correct option is D 10 angstrom

Given,

${\lambda }_H=1216angstrom$, $Z_H=1$

For $N{a}^{+10},Z_{Na}=11$

From the Bohr's theory,

$R=\frac{hc}{\lambda }=R{Z}^2(\frac{1}{n_f^2}-\frac{1}{n_i^2})$

$\lambda \propto \frac{1}{Z^2}$

So, $\frac{{\lambda }_{Na}}{{\lambda }_H}=(\frac{Z_H}{Z_{Na}}{)}^2=\frac{1\times 1}{11\times 11}$

${\lambda }_{Na}=\frac{1216}{11\times 11}$

${\lambda }_{Na}=10angstrom$

The correct option is D.