The ground state energy of hydrogen atom is -13.6 eV. If an electron makes a transition from an energy level -0.85 eV to -0.74 eV, calculate the wavelength of the spectral line emitted. To which series of hydrogen spectrum does the wavelength belong?

For hydrogen atom we know that En = -13.6/n²

Now for the transition from En1 = -0.85 to En2 = -0.74,
-0.85 = -13.6/n₁² or n₁² = 16 or n₁ = 4
and -0.74 = -13.6/n₂² or n₂ = 2

Using, 1/λ = R(1/n₂² - 1/n₁²)
we get 1/λ = (1.097 × 10⁷ m⁻¹)(1/2² - 1/4²)
or λ = 4.86 × 10⁻⁷ m

As the electron makes the transition from n=4 to n=2 so it will be Balmer series.