Final answer:
The claim is false; two different sodium lamps emitting light of the same wavelength will typically not produce an interference pattern because the light from each lamp is not coherent.
Step-by-step explanation:
The statement that no interference pattern will be observed on the screen in Young's double slit experiment when the slits are illuminated by two different sodium lamps emitting light of the same wavelength is false.
For an interference pattern to be formed in Young's experiment, the light sources need to be coherent, meaning they must have a constant phase difference. Normally, this is achieved by using light from a single source which is then split into two paths to create two coherent sources.
The use of two separate sodium lamps, even if they emit the same wavelength of light, typically will not produce coherent light sources because the phases of the individual lamps' emissions vary independently over time, causing the interference pattern to be washed out.
Thus, an interference pattern is unlikely to be seen with two different sodium lamps in Young's double slit experiment, as the necessary coherence is absent.