Q: A 12.5 eV electron beam is used to bombard gaseous hydrogen at room temperature. What series of
wavelength will be emitted ?
Sol: Energy of electron beam E = 12.5 eV
= 12.5 × 1.6 × 10-10 J
Planck’s constant h = 6.63 × 10-34 j-s
Velocity of light c = 3 × 108 m/s
Using the relation E = hc/λ , λ = (6.62 × 10-34 × 3 × 108)/(12.5 ×1.6 × 10-19 )
= 0.993 × 10-7 m = 993 × 10-10 m = 993 A°
This wavelength falls in the range of Lyman series (912 A° to 1216 A°)
Thus, we conclude that Lyman series of wavelength 993 A° is emitted.