Question

The wavelength (in $\mathring{A}$ ) of an emission line obtained for $Li ^{2+}$ during a electronic transition from $n _{2}=2$ to $n _{1}=1$ is: $( R =$ Rydberg constant $)$

• A. $3 R / 4$
• B. $27 R / 4$
• C. $4 / 3 R$
• D. $4 / 27 R$

Answer 1

Answer: (D)

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

where, $R_{H}=R, Z=3\left(\right.$ for $L i^{2+},$ atomic no. $\left.3\right)$

$n_{2}=2, n_{1}=1$

$\frac{1}{\lambda} = R (3)^{2}\left(\frac{1}{(1)^{2}}-\frac{1}{(2)^{2}}\right)$

$=\frac{ R \times 9 \times 3}{4}$

$\Rightarrow \lambda=\frac{4}{27 R }$