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

(D) For the first line of the Lyman series of hydrogen $(n_1=1, n_2=2)$:$\frac{1}{\lambda_1} = R(1)^2 \left(\frac{1}{1^2} - \frac{1}{2^2}\right) = R \

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(D) For the first line of the Lyman series of hydrogen $(n_1=1, n_2=2)$:$\frac{1}{\lambda_1} = R(1)^2 \left(\frac{1}{1^2} - \frac{1}{2^2}\right) = R \left(1 - \frac{1}{4}\right) = \frac{3R}{4}$For the second line of the Balmer series of a hydrogen-like ion $(n_1=2, n_2=4)$:$\frac{1}{\lambda_2} = R Z^2 \left(\frac{1}{2^2} - \frac{1}{4^2}\right) = R Z^2 \left(\frac{1}{4} - \frac{1}{16}\right) = R Z^2 \left(\frac{3}{16}\right)$Given that $\lambda_1 = \lambda_2$,we have $\frac{1}{\lambda_1} = \frac{1}{\lambda_2}$:$\frac{3R}{4} = \frac{3RZ^2}{16}$Dividing both sides by $\frac{3R}{4}$:$1 = \frac{Z^2}{4}$$Z^2 = 4$$Z = 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

If $a^x = b$,$b^y = c$,and $c^z = a$,then the value of $xyz$ is:

How many different types of gametes will be produced by a plant with the genotype $AABbCC$?

$A$ group of atoms can function as a ligand only when

The electron affinity of sulfur is........

Vedclass Test Series

Exam Paper Generator

Online Exam Module