Question

Assertion (A): In Lyman series of H-spectra, the maximum wavelength of the lines is $ 121.56 $ nm.
Reason (R): Wavelength is maximum when the transition is from the very next level.
(A) Both A and R are true and R is the true explanation of A.
(B) Both A and R are true, but R not the true explanation of A.
(C) A is true, but R is false.
(D) A is true but R is false.

Answer 1

Hint: The transition of the electron from one level to the other is dependent upon the difference of energy between the two energy levels among which the transition is caused. It is calculated using the Rydberg constant.

Complete Stepwise Solution:
When the hydrogen atom absorbs the energy from a source of radiation then the electron jumps to the higher orbitals and after a certain time the electron again returns to the ground state emitting radiation, the wavelength of which depends upon the energy level to which the electron was excited to. The energy of the orbitals on the other hand is dependent on the frequency and the wavelength of the radiation as such that the higher the frequency of energy, lower will be its wavelength and vice versa. As the first transition of the Lyman series is from the first shell to the second shell, the energy difference will be less and hence that transition will be of maximum wavelength. $ \frac{1}{\lambda } = 109678\left( {\dfrac{1}{{{{\text{n}}_1}^2}} - \dfrac{1}{{{\text{n}}_2^2}}} \right) $ , $ \lambda $ is the wavelength of radiation.
Putting the values of and, we get, $ \dfrac{1}{\lambda } = 109678\left( {\dfrac{1}{{{1^2}}} - \dfrac{1}{{{2^2}}}} \right) = 109678 \times \dfrac{3}{4} = 0.000012156 = 121.56 \times {10^{ - 9}} $ m.
Hence the maximum wavelength of the Lyman series is $ 121.56 $ nm and this is due to the transition from the very next level.
So the first option is correct, Both A and R are true and R is the true explanation of A.

Note:
The series of light radiations of different wavelengths that are emitted from the hydrogen atom are called the hydrogen spectrum. Depending on the wavelength of the radiation, there are five series of emission lines by the hydrogen atom. When the transition is from the first shell to any other higher orbital, then is called the Lyman series, when the transition is from the second shell to any other higher orbital, then is called the Balmer series, when the transition is from the third shell to any other higher orbital, then is called the Paschen series, when transition is from the fourth shell to any other higher orbital, then is called the Brackett series, lastly, when the transition is from the fifth shell to any other higher orbital, then is called the Pfund series.