Question

The wavelength of the first line of Lyman series in a hydrogen atom is $1216A^0$. The wavelength of the first line of Lyman series for $10$ times ionised sodium atom will be:

• A. $0.1A^0$
• B. $1000A^0$
• C. $100A^0$
• D. $10A^0$

Answer 1

The correct option is D $10A^0$

$\frac{hc}{\lambda }={\frac{-13.6}{n}}^2$ where $n=1$
$\to \lambda =\frac{-13.6}{hc}=\lambda =\frac{-hc}{13.6}=1216A^0$
Now, wavelength for 10 times ionised sodium atom, The ${10}^{th}$ ionised sodium atom is taken from $n=1$, the most internal atoms.
$\Rightarrow \frac{hc}{\lambda }=-13.6(11{)}^2$
$(1{)}^2$
$\Rightarrow \frac{hc}{(11{)}^{2}13.6}=\lambda$

$\Rightarrow \lambda =\frac{1216A^0}{121}$
$\Rightarrow \lambda =10.049A^0$
$\Rightarrow \lambda =10A^0$