Question

A xenon arc lamp is covered with an interference filter that only transmits light of 400-nm wavelength. When the transmitted light strikes a metal surface, a stream of electrons emerges from the metal. The interference filter is then replaced with one transmitting at 300 nm and the lamp adjusted so that the intensity of the light striking the surface is the same as it was for the 400-nm light. With the 300- nm light 1. more electrons are emitted in a given time interval. 2. the electrons which are emitted are more energetic 3. both are true. 4. both are false. Please choose from 1-4, explaining your answer.

Answer 1

3. Both are true

Step-by-step explanation:

This is because the number of electrons emitted and their energy does not depend on intensity but on the wavelength. From K.E = hc/λ - Φ where λ = wavelength, Φ = work function and hc/λ = energy of the incoming light

Electrons are emitted when hc/λ > Φ. Since the energy of the incoming light is inversely proportional to its wavelength, for the 300 nm light, there is more energy and thus the difference hc/λ - Φ is more than that of the 400 nm light thereby releasing more electrons.

Also, since the difference hc/λ - Φ is more than that of the 400 nm light the kinetic energy K.E of the electrons is also more in this instant. So the electrons emitted are more energetic.

Answer 2

3. both are true.

Step-by-step explanation:

Energy increses with decrease in wavelenght.

For photoemission to occur, a threshold energy barrier must be broken.

Higher energy means more electrons will be emmited.

The electrons emmited will posses energy that is less than the incident energy by the value of the threshold energy.

So the higher the energy, the higher the energy possessed by the electrons.