The difference in wavelength of first and sec | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) For a hydrogen-like species,the Rydberg formula is given by: $\frac{1}{\lambda} = R Z^2 (\frac{1}{n_1^2} - \frac{1}{n_2^2})$.For the Lyman series,

Vedclass · Accepted Answer

$21.1$

Vedclass · Answer

(D) For a hydrogen-like species,the Rydberg formula is given by: $\frac{1}{\lambda} = R Z^2 (\frac{1}{n_1^2} - \frac{1}{n_2^2})$.For the Lyman series,$n_1 = 1$. For $Li^{2+}$,$Z = 3$.First line of Lyman series ($n_1 = 1$ to $n_2 = 2$): $\frac{1}{\lambda_1} = R (3)^2 (\frac{1}{1^2} - \frac{1}{2^2}) = 9R (1 - \frac{1}{4}) = 9R (\frac{3}{4}) = \frac{27R}{4}$. So,$\lambda_1 = \frac{4}{27R}$.Second line of Lyman series ($n_1 = 1$ to $n_2 = 3$): $\frac{1}{\lambda_2} = R (3)^2 (\frac{1}{1^2} - \frac{1}{3^2}) = 9R (1 - \frac{1}{9}) = 9R (\frac{8}{9}) = 8R$. So,$\lambda_2 = \frac{1}{8R}$.Given $R \approx 1.097 	imes 10^7 \ m^{-1} = 1.097 	imes 10^{-2} \ \mathring{A}^{-1}$.$\lambda_1 = \frac{4}{27 	imes 1.097 	imes 10^{-2}} \approx 135.05 \ \mathring{A}$.$\lambda_2 = \frac{1}{8 	imes 1.097 	imes 10^{-2}} \approx 113.95 \ \mathring{A}$.Difference $\Delta \lambda = \lambda_1 - \lambda_2 = 135.05 - 113.95 = 21.1 \ \mathring{A}$.

The difference in wavelength of first and second spectral lines of Lyman series in $Li^{2+}$ ion spectrum is ................ $\mathring{A}$

Similar Questions

One energy difference between the states $n = 2$ and $n = 3$ is $E \ eV$,in a hydrogen atom. The ionization potential of the $H$ atom is ............. $E$.

The ionization enthalpy of a hydrogen atom is $1.312 \times 10^6 \, J \, mol^{-1}$. The energy required to excite an electron from $n = 1$ to $n = 2$ in the atom is .......

For a $H$ atom,the wavelength for the highest energy transition is $91.2 \ nm$. Calculate the corresponding wavelength for $He^{+}$ in $nm$.

The radii of the first Bohr orbit of $H$ $(r_{H})$,$He^{+}$ $(r_{He^{+}})$ and $Li^{2+}$ $(r_{Li^{2+}})$ are in the order

The total number of spectral lines observed when an electron returns from the $6^{th}$ shell to the $2^{nd}$ shell in a hydrogen atom is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module