Test: Hydrogen Spectrum (April 22) - JEE MCQ

The Balmer series just sets n₁ = 2, which means the value of the principal quantum number (n) is two for the transitions being considered. Balmer’s formula can therefore be written:

1/λ = R_H ((1/2²) − (1 / n₂²))

1/wavelength =RH x z² x (1/2²-1/5²) =109677 x 1 x (1/4-1/25) =109677 x 21/100 =2303.2m wavelength=1/2303.2m =1/2303.2 x 10⁷nm =434.1nm~434nm

The negative sign means that the energy of the electron in the atom is lower than the energy of a free electron at rest. A free electron at rest is an electron that is infinitely far away from the nucleus and is assigned the energy value zero.

Light not absorbed by the sample will, as before, be separated (dispersed) into its component wavelengths (colors) by the prism. The appearance of the spectrum will resemble that obtained without the sample in place, with the exception that those wavelengths which have been absorbed are missing, and will appear as dark lines within the spectrum of colors. If a piece of the photographic film is used instead of the card, the absorption spectrum can be recorded.

using the formula:

E = h.v

= 6.63 x 10^-34 x 5.1 x 10¹⁴

= 33.8 x 10^-20 J

The formula to calculate the excitation energy is 13.6Z²(1/n1²-1/n2²), but this gives value in eV. To convert it in Joules we divide it by 6.24×10¹⁸ Here, Z=1,n1=1,n2=3 Putting these values in above formula we have, [13.6×1(1-1/9)]/6.24×10¹⁸ =(13.6×8×10^-18)/(9×6.24) =1.94×10^-18 Hence, the correct answer is C.

Paschen series from n = 4, 5, 6, 7……to n = 3

For hydrogen Z=1,
and n is given as 1,
Then
E= -13.6 × n power 2/ Z.
E= - 13.6 × 1 power 2/ 1.
E= -13.6e.v.

The Zeeman effect is the splitting of the spectral lines of an atom in the presence of a strong magnetic field. The effect is due to the distortion of the electron orbitals because of the magnetic field. The (normal) Zeeman effect can be understood classically, as Lorentz predicted.