If the shortest wavelength of the He^{+} ion | vedclass

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

Question

(B) The Rydberg formula is given by $\frac{1}{\lambda} = R Z^2 \left(\frac{1}{n_1^2} - \frac{1}{n_2^2}\right)$.For the shortest wavelength in the Balm

Vedclass · Accepted Answer

$\frac{16}{7} \ X$

Vedclass · Answer

(B) The Rydberg formula is given by $\frac{1}{\lambda} = R Z^2 \left(\frac{1}{n_1^2} - \frac{1}{n_2^2}ight)$.For the shortest wavelength in the Balmer series of $He^{+}$ $(Z=2)$: $n_1 = 2$,$n_2 = \infty$.$\frac{1}{X} = R 	imes 2^2 \left(\frac{1}{2^2} - \frac{1}{\infty^2}ight) = R 	imes 4 	imes \frac{1}{4} = R$.So,$R = \frac{1}{X}$.For the longest wavelength in the Paschen series of $Li^{2+}$ $(Z=3)$: $n_1 = 3$,$n_2 = 4$.$\frac{1}{\lambda_{Li^{2+}}} = R 	imes 3^2 \left(\frac{1}{3^2} - \frac{1}{4^2}ight) = R 	imes 9 \left(\frac{1}{9} - \frac{1}{16}ight) = R 	imes 9 \left(\frac{16-9}{144}ight) = R 	imes 9 	imes \frac{7}{144} = R 	imes \frac{7}{16}$.Substituting $R = \frac{1}{X}$:$\frac{1}{\lambda_{Li^{2+}}} = \frac{1}{X} 	imes \frac{7}{16} \implies \lambda_{Li^{2+}} = \frac{16}{7} \ X$.

If the shortest wavelength of the $He^{+}$ ion in the Balmer series is $X \ m$,then the longest wavelength in the Paschen series of the $Li^{2+}$ ion is:

Similar Questions

The time taken for an electron to complete one revolution in Bohr orbit of hydrogen atom is

The Bohr orbit radius for the hydrogen atom $(n = 1)$ is approximately $0.530 \ \mathring{A}$. The radius for the first excited state $(n = 2)$ orbit is ........... $\mathring{A}$

What is the number of waves formed by an electron in the $5^{th}$ Bohr orbit of a hydrogen atom?

When electronic transition occurs from a higher energy state to a lower energy state with an energy difference equal to $\Delta E$ electron volts,the wavelength of the emitted line is approximately equal to

$A$ surface ejects electrons when hit by green light but not when hit by yellow light. Will electrons be ejected if the surface is hit by red light?

Vedclass Test Series

Exam Paper Generator

Online Exam Module