Single Choice

In the spectrum of hydrogen, the ratio of the longest wavelength in the Lyman series to the longest wavelength in the Balmer series is:

A$$\displaystyle \frac{5}{27}$$
Correct Answer
B$$\displaystyle \frac{4}{9}$$
C$$\displaystyle \frac{9}{4}$$
D$$\displaystyle \frac{27}{5}$$

Solution

Transition to $$n=1$$ and $$n=2$$ are refered to as Lyman and Balmer series.

For Lyman Series wavelength will be longest when energy the electron has transition from $$n=2$$ to $$n=1$$ level.
For Balmer Series wavelength will be longest when energy the electron has transition from $$n=3$$ to $$n=2$$ level.
$$E_2 -E_1 \propto (- \dfrac{1}{1^2} + \dfrac{1}{2^2} ) = \dfrac{3}{4}$$
$$E_3 -E_2 \propto (- \dfrac{1}{3^2} + \dfrac{1}{2^2} ) = \dfrac{5}{36}$$
$$\dfrac{E_2 -E_1 }{E_3 -E_2 } = \dfrac{\dfrac{3}{4}}{ \dfrac{5}{36}}=\dfrac{27}{5}$$
Hence, $$ \dfrac{\lambda _L } {\lambda _B}=\dfrac{5}{27}$$ as $$E \propto \dfrac{1}{\lambda}$$

SIMILAR QUESTIONS

Nuclear Physics

If the series limit wavelength of Lyman series for the hydrogen atom is $$912\overset {\circ}{A}$$, then the series limit wavelength for Balmer series of hydrogen atoms is

Nuclear Physics

If an electron in a hydrogen atom jumps from the 3rd orbit to the 2nd orbit, it emits a photon of wavelength $$\lambda$$. When it jumps from the 4th orbit to the 3rd orbit, the corresponding wavelength of the photon will be

Nuclear Physics

The ratio of wavelengths of the last line of Balmer series and the last line of Lyman series is

Nuclear Physics

Ratio of longest wavelengths corresponding to Lyman and Balmer series in hydrogen spectrum is

Nuclear Physics

The wavelengths of $$K_\alpha$$ X-rays for lead isotopes $$Pb^{208}, Pb^{206}$$ and $$Pb^{204}$$ are $$\lambda_1, \lambda_2$$ and $$\lambda_3$$ respectively. Then

Nuclear Physics

Black holes in orbit around a normal star are detected from the earth due to the frictional heating of infalling gas into the black hole, which can reach temperatures greater than $$10^6K$$.Assuming that the infalling gas can be modelled as a black body radiator, then the wavelength of maximum power lies

Nuclear Physics

The series corresponding to minimum wave length transition in H-atom is

Nuclear Physics

Balmer gives an equation for wavelength of visible radiation of H spectrum as $$\lambda = \dfrac{kn^2}{n^2 - 4}$$. The value of k in terms of Rydberg's constant R is

Nuclear Physics

The wavelength of an electron for transition from a state $$n_{1}$$ to $$n_{2}$$ is $$\displaystyle\frac{9}{8R}$$. Which of the following wavelengths is possible for a transition from $$n_{2}$$ to $$n_{1}$$

Nuclear Physics

The frequencies for series limit of Balmer and Paschen series respectively are $$'v_{1}'$$ and $$'v_{3}'$$. If frequency of first line of Balmer series is $$'v_{2}'$$ then the relation between $$'v_{1}', 'v_{2}'$$ and $$'v_{3}'$$ is

Contact Details