A 12.9 eV beam of electrons is used to bombard gaseous hydrogen at room temperature. Up to which energy level would the hydrogen atoms be excited?

n=4 as energy difference between n=1 and n=4 is 12.75 eV.
For first wavelength of Balmer series:
hc/λ₁ = (13.6eV)(1/2² - 1/4²) ≈ 1240 eV.nm
λ₁ = 13.6 × 36/4 ≈ 1240 × 36 / 13.6 nm = 656.4 nm = 6564 Å
For first wavelength of Paschen series:
hc/λ'₁ = (13.6eV)(1/3² - 1/4²) ≈ 1240 eV.nm
λ'₁ = 13.6 × 144/7 ≈ 1240 × 144 / (7 × 13.6) nm = 1875.6 nm = 18756 Å