Light from three different lasers (a, b, and c), each with a different wavelength, was shined on the same metal surface. laser a produced no photoelectrons. lasers b and c both produced photoelectrons, but those produced by b had a greater velocity than those produced by c. arrange the lasers in order of increasing wavelength.
if a didn't produce any photoelectrons, wouldn't it just be a straight line with the highest frequency? and to have a greater velocity would that mean the wavelength increases frequency?

Explanation:

It is known that each metal has a different work function and it is just the energy required to remove the electron from the surface.

The relation between energy and work function is as follows.

where,   = energy of photon

               Q = work function

             K.E = kinetic energy of electron

When the value of Q is large then the amount of energy required by the photon is also large and vice-versa.

And, when there is not sufficient energy to remove an electron from metal surface or energy is less than its work function then electron will not be removed.

On the other hand, when incoming photon will have enough energy then electron will be ejected.

In the given situation, light from laser A is not able to remove the electron from metal surface which means that energy of photon is less than work function Q.

As, both B and C are able to remove electron from the surface of metal. So, after the removal of electrons rest of the energy of photons is transferred to eject electrons and this energy is converted into kinetic energy.

As energy of B is greater than the energy of C and A has the lowest energy among all.

Therefore, order of energy from lowest to highest is as follows.

                              A < C < B

Now, the relation between energy and wavelength is as follows.

                   E =

where,     = wavelength

So, energy is inversely proportional to wavelength. Therefore, increase in energy means decrease in wavelength.

Therefore, increasing order of wavelength is as follows.

                            B < C < A

catya that's not even a b or c