The work function of sodium in Joules is:
Φ=2.3×1.6×10−19=3.68×10−19 J
The kinetic energy of the ejected electrons is:
K=2.8×10−20=0.28×10−19 J
Using the photoelectric equation, the energy of the incident photon is:
E=Φ+K
E=3.68×10−19+0.28×10−19=3.96×10−19 J
The wavelength of the incident radiation is calculated using E=λhc:
λ=Ehc=3.96×10−196.6×10−34×3.0×108
λ=3.96×10−1919.8×10−26=5×10−7 m
Converting the wavelength to nanometers:
λ=500×10−9 m =500 nm
Given that the wavelength is x nm, we get x=500.
Expressing x in the required format:
x=5×102
The value to be filled in the blank is 5.
Answer: 5