The difference in energy levels of an electron at two excited levels is 13.75 ~eV . If it makes a transition from the higher energy level to the lower energy level then what will be the wave length of the emitted radiation? [given h=6.6 10⁻³⁴ ~m ^2 ~kg ~s ⁻¹ ; c=3 10^8 ~ms ⁻¹ ; 1 ~eV =1.6 10⁻¹⁹ ~J ]

Step-by-step solution

The energy difference between the two levels is given by E = 13.75 eV . Converting this energy into Joules: E = 13.75 1.6 10⁻¹⁹ J = 22 10⁻¹⁹ J . The relationship between energy and wavelength is E = hc . Rearranging for wavelength : = hc E . Substituting the given values h = 6.6 10⁻³⁴ J s and c = 3 10^8 m/s : = 6.6 10⁻³⁴ 3 10^8 22 10⁻¹⁹ . = 19.8 10⁻²⁶ 22 10⁻¹⁹ = 0.9 10⁻⁷ m . Converting to Angstroms ( A ): = 0.9 10⁻⁷ 10¹⁰ A = 0.9 10^3 A = 900 A . Answer: 900^ A