Electromagnetic Radiation Theory & Math Questions help please

[skg94]

Homework Statement

1. Explain the effects
To the photocurrent as the light intensity increases
To the photocurrent as the frequency of the light is increased
To the speed of the photoelectrons as the radiation intensity increases
To the speed of the photelectrons as the radiation frequency increases

2. Radiation with a frequency of 6.67 * 10^14 Hz is used to illuminate a photoelectric surface (W=2.50eV). The ejected electrons are now deflected by a perpendicular magnetic field (B=3.11*10^-5T). What is the maximum radius of these deflected electrons? [ANS: 5.57 * 10^-2m ]

Homework Equations

Ek = hf-W
W=hfo
c=f (lambda - wavelength)

The Attempt at a Solution

1.a) more current
b) nothing
c) increases speed
d) increases speed - i don't really know how do i solve this? some help here


2. I really have no idea

i got E, from E=hf-W = 4.2221 *10^-20, but i don't know how to fuse B with E to find radius, maybe Fm=Fc? but so many unknowns.

 

[kvnstv1]

In response, to question 1,

1. As your intensity of light increases, the NUMBER of photons hitting the surface of your material will increase. Thus, the number of electrons emitted will increase, and, as you have said, increase the current.

2. Keeping mind the presence of the threshold frequency, which is the minimum energy each photons have to give to a metal to enable the emission of an electron, understand intuitively that increasing the energy of a photon will not affect the number of electrons released. There will be a spike from 0 at the threshold frequency, but otherwise, the current is unaffected.

3. As the number of photons hitting a metal surface increases (i.e. as Intensity increases) the kinetic energy given to each electron is unaffected, even though more electrons are emitted. Thus, speed is unaffected.

4. As radiation frequency increases, obviously, more energy is given to an electron, which, after allowing it to break free from the surface of the metal, gives it Kinetic Energy, which shows in the form of greater speed.

What is probably confusing you is the relationship between Energy and Frequency. Remember the formula E=Hf, where E is energy, h is the Planck Constant and f is the frequency of the wave.

 

[skg94]

Ah true applying it to the formula is easiest, so as intensity increases. current increases but speed remains the same, as frequency increases current reamains the same while speed increases - is that correct?

 

[skg94]

Anyone know how to do question 2?

 

[ap123]

The value you've calculated for E is the kinetic energy of the photoelectron.
Work out the speed of the electron from this.

The force on the electron in the magnetic field is
F = evB.

This force holds the electron in a circular path, so it's the centripetal force.

If you use the formula for the centripetal force, you should be able to calculate the radius.