The short wavelength limit for the Lyman series of the hydrogen spectrum is 913.4......................

Question 4:The short wavelength limit for the Lyman series of the hydrogen spectrum is 913.4 A0 . Calculate the short wavelength limit for the Balmer series of the hydrogen spectrum.

The correct answer is - The Balmer series of the hydrogen spectrum consists of the spectral lines that result from electronic transitions between the excited states of hydrogen atoms and the n=2 energy level. The shortest wavelength limit for the Balmer series corresponds to the transition from the third energy level (n=3) to the second energy level (n=2). This is known as the Balmer limit.

The energy of a hydrogen atom in the nth energy level is given by the formula:

E_n = -13.6 eV / n^2

where eV represents electron volts, a unit of energy.

The difference in energy between the n=3 and n=2 energy levels is:

ΔE = E_3 - E_2 = (-13.6 eV / 3^2) - (-13.6 eV / 2^2) = 1.51 eV

To convert this energy difference to a wavelength, we can use the formula:

λ = hc / ΔE

where λ is the wavelength, h is Planck's constant, and c is the speed of light.

Substituting the values, we get:

λ = (6.626 x 10^-34 J s) x (2.998 x 10^8 m/s) / (1.51 eV x 1.602 x 10^-19 J/eV) = 364.6 nm

Converting this to angstroms, we get:

λ = 364.6 nm x 10 A/nm = 3646 Å

Therefore, the short wavelength limit for the Balmer series of the hydrogen spectrum is 3646 Å.