If the longest wavelength of the spectral lin | vedclass

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

Question

(B) The Rydberg formula is given by $\frac{1}{\lambda} = R_H 	imes Z^2 	imes (\frac{1}{n_1^2} - \frac{1}{n_2^2})$.For the longest wavelength of the

Vedclass · Accepted Answer

$\frac{7}{12} x$

Vedclass · Answer

(B) The Rydberg formula is given by $\frac{1}{\lambda} = R_H 	imes Z^2 	imes (\frac{1}{n_1^2} - \frac{1}{n_2^2})$.For the longest wavelength of the Paschen series of $Li^{2+}$ $(Z=3)$,we have $n_1 = 3$ and $n_2 = 4$.$\frac{1}{x} = R_H 	imes (3)^2 	imes (\frac{1}{3^2} - \frac{1}{4^2}) = R_H 	imes 9 	imes (\frac{1}{9} - \frac{1}{16}) = R_H 	imes 9 	imes \frac{7}{144} = R_H 	imes \frac{7}{16}$.Thus,$x = \frac{16}{7 R_H}$ ...$(i)$.For the longest wavelength of the Lyman series of the hydrogen spectrum $(Z=1)$,we have $n_1 = 1$ and $n_2 = 2$.$\frac{1}{\lambda} = R_H 	imes (1)^2 	imes (\frac{1}{1^2} - \frac{1}{2^2}) = R_H 	imes (1 - \frac{1}{4}) = R_H 	imes \frac{3}{4}$.Thus,$\lambda = \frac{4}{3 R_H}$ ...$(ii)$.Dividing equation $(ii)$ by equation $(i)$:$\frac{\lambda}{x} = \frac{4 / (3 R_H)}{16 / (7 R_H)} = \frac{4}{3} 	imes \frac{7}{16} = \frac{7}{12}$.Therefore,$\lambda = \frac{7}{12} x$.

If the longest wavelength of the spectral line of the Paschen series of $Li^{2+}$ ion spectrum is $x \ \mathring{A}$,then the longest wavelength (in $\mathring{A}$) of the Lyman series of the hydrogen spectrum is

Similar Questions

The frequency of radiation emitted when the electron falls from $n = 4$ to $n = 1$ in a hydrogen atom will be (Given $h = 6.625 \times 10^{-34} \, J s$):-

Suppose the ionization energy of a hydrogen-like species is $960 \ eV$. The value of the principal quantum number for an energy level of $-60 \ eV$ will be $......$.

When a metal surface is exposed to a certain frequency of electromagnetic radiation,the kinetic energy of the electron ejected from the metal surface is $0.20 \ eV$. If its work function $(W_0)$ is $4.80 \ eV$,the approximate frequency of the radiation falling on the metal surface in $Hz$ is:

Find the wavelength in the Lyman series for $n_2 = 3$ and $n_1 = 1$.

If the threshold wavelength for a metal is $\lambda_0$ and the wavelength of incident light is $\lambda$,what will be the maximum velocity of the emitted electrons?

Vedclass Test Series

Exam Paper Generator

Online Exam Module