We know from Rydberg's Equation, the wavelength λ of emission spectrum when electrons move from n₂ energy level to n₁ energy level is given by,

For Hydrogen atom, Z=1.

The wavelength range 380-780 nm lies in the Balmer Series.

Thus, n₁=2 for Balmer Series.

Substituting n₂=3, we get λ=656.3 nm

Substituting n₂=7, we get λ=397.0 nm

Thus, we get 5 wavelengths: n=3 to n=2; n=4 to n=2; n=5 to n=2; n=6 to n=2 and n=7 to n=2.

For other values of n₂, the range of 380-780nm is not possible.

The wavelength range 50-100 nm, within n=7 to n=2, lies in the Lyman Series.

Thus, n₁=1 for Lyman Series.

Substituting n₂=4, we get λ=97.3 nm

Substituting n₂=6, we get λ=93.8 nm

Thus, we get 3 wavelengths: n=4 to n=1; n=5 to n=1 and n=6 to n=1.

For other values of n₂ (within n=7 to n=2), the range of 50-100 nm is not possible.