The wavelength of the first line of the Lyman | vedclass

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

Question

(B) The wavelength $\lambda$ of the first line of the Lyman series for a hydrogen atom $(Z=1)$ is given by the Rydberg formula:$\frac{1}{\lambda} = R(

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(B) The wavelength $\lambda$ of the first line of the Lyman series for a hydrogen atom $(Z=1)$ is given by the Rydberg formula:$\frac{1}{\lambda} = R(1)^2 \left[ \frac{1}{1^2} - \frac{1}{2^2} \right] = R \left[ 1 - \frac{1}{4} \right] = \frac{3R}{4}$The wavelength $\lambda'$ of the second line of the Balmer series for a hydrogen-like ion with atomic number $Z$ is given by:$\frac{1}{\lambda'} = R Z^2 \left[ \frac{1}{2^2} - \frac{1}{4^2} \right] = R Z^2 \left[ \frac{1}{4} - \frac{1}{16} \right] = R Z^2 \left[ \frac{4-1}{16} \right] = \frac{3 R Z^2}{16}$According to the problem,$\lambda = \lambda'$,which implies $\frac{1}{\lambda} = \frac{1}{\lambda'}$:$\frac{3R}{4} = \frac{3 R Z^2}{16}$Dividing both sides by $\frac{3R}{4}$:$1 = \frac{Z^2}{4}$$Z^2 = 4$$Z = 2$Thus,the atomic number of the hydrogen-like ion is $2$.

The wavelength of the first line of the Lyman series for a hydrogen atom is equal to that of the second line of the Balmer series for a hydrogen-like ion. The atomic number $Z$ of the hydrogen-like ion is:

Similar Questions

In the line spectra of the hydrogen atom,the difference between the largest and the shortest wavelengths of the Lyman series is $304\,\mathring{A}$. The corresponding difference for the Paschen series in $\mathring{A}$ is:

Line spectra are due to

In a hydrogen sample,if the atoms are excited to states with principal quantum number $n = 20$,then the number of different wavelengths which may be observed in the spectrum is:

In a hydrogen atom,when an electron transitions from the fourth orbit to the ground state,find the wavelength of the emitted photon in $nm$.

The ratio of longest wavelengths of the spectral lines in the Lyman and Balmer series of hydrogen spectrum is

Vedclass Test Series

Exam Paper Generator

Online Exam Module