In: Physics

A 20 mW 360 nm laser is incident on a metal anode. The metal in
the anode has a work

function of 1.80 eV.

a) What voltage must be applied to completely stop the
photo-electrons?

b) In the absence of an applied voltage, what current would be
measured? assuming

i) all photons in the laser produce a photo-electron and

ii) all photo-electrons reach the cathode

c) Why are these unrealistic assumptions?

d) What is the deBroglie wavelength of the emitted electrons?

For the external photoelectric effect we have

Photon energy = Work function + Electron kinetic energy

h*F = W + Ek

h*F = W +eU

where U is the stopping potential that need to be applied to completely stop all electrons

**U =[(h*c/lambda)-W)/ e** =
6.62*10^-34*3*10^8/360*10^-9/1.6*10^-19 - 1.8 **=1.648
V**

If N/t is number of photons in time unit then

Power = Energy/time = (N/t) h*F = (N/t)*(h*c/lambda)

N/t = P*lambda/(h*c) = 0.02*360*10^-9/6.62*10^-34/3*10^8 =3.62*10^16 photons/sec

If 1 photon = 1 electron emitted then current is

**I = Q/t = (N/t)*e =**3.62*10^16*1.6*10^-19
=5.8*10^-3 A **=5.8 mA**

These are unrealistic assumption because of two main reasons:

- efficiency of photoelectric effect is ussualy 5-20%.

- electrons emitted in their way to cathode scatter on wir molecules that remain in tube and do not reach the cathode. The vacuum in the tube need to be less than 10^-9 Torr. (Ultra high vacuum)

De Broglie wavelength is

**lambda = h/p = h/sqrt(2*m*Ek) = h/sqrt(2*m*e*U)
=**6.62*10^-34/sqrt(2*9.1*10^-31*1.6*10^-19*1.648)
**=9.56*10^-10 m**

A beam of wavelength 310 nm from a laser is incident on a metal
with work function 2.7 eV. The power of the laser is 0.15 W.
(a) Does the metal emit photoelectrons? Why?
(b) What is the range of photoelectron kinetic energies emitted
by metal?
(c) What is the range of de Broglie wavelengths of these
photoelectons?
(d) How does result for part (b) change if the laser power is
doubled to 0.30 W?
Thank you.

A laser of wavelength 200 nm is incident on a metal surface,
which causes the ejection of electrons. The stopping potential is
measured to be 1.66 V.
Use the table below to identify the metal.
Copper
Sodium
Aluminum
Iron
Tungsten

A green laser operates at 488.0 nm with an output
power of 2.5 mW. Calculate the average output in photons/s (“photon
flux”). What would the output power be for the same flux of 244.0
nm photons? What would the photon flux be for a 488.0 nm laser
operating at 5.0 mW?

A laser beam with vacuum wavelength 582 nm is incident from air
onto a block of Lucite as shown in the figure below. The line of
sight of the photograph is perpendicular to the plane in which the
light moves. Take θ1 to be 60°. Recall that the index of refraction
of air is 1 and Lucite is 1.50. (a) Find the speed of the light in
Lucite.. m/s (b) Find the frequency of the light in Lucite.. Hz (c)...

A small He-Ne laser produces a 632.8 nm beam with an average
power of 3.5 mW and diameter of 2.4mm
a) How many photons per second are emitted by the laser?
b) What is the amplitude of the electric field inside the beam?
(Hint: You should consult your EP book, the internet, or equation
3.10 for this problem)
c) How does this electric field compare with one produced by a 100W
light bulb at a distance of 1 meter?

When light of wavelength 400 nm is incident on a metal surface,
the stopping
potential of the photoelectrons is 0.600 V.
a. What is the work function of the metal?
b. What is the threshold frequency?
c. What is the maximum kinetic energy of the electron?

When light with a wavelength of 247 nm is incident on a certain
metal surface, electrons are ejected with a maximum kinetic energy
of 2.84 × 10-19 J. Determine the wavelength (in nm) of
light that should be used to double the maximum kinetic energy of
the electrons ejected from this surface.

When light with a wavelength of 215 nm is incident on a certain
metal surface, electrons are ejected with a maximum kinetic energy
of 3.33 × 10 − 19 J. Determine the wavelength of light that should
be used to quadruple the maximum kinetic energy of the electrons
ejected from this surface.

White light (ranging in wavelengths from 380 to 750 nm) is
incident on a metal with work function Wo = 2.68 eV.
1. For what range of wavelengths (from lmin to
lmax) will NO electrons be emitted?
a) Imin=
b) Imax=

Light from a red laser (650 nm) is incident on two slits
separated by 0.5 mm. Each slit is 0.25 mm wide. Quantitatively
sketch the pattern you would observe on a screen that is located
2.0 m from the slits. Your sketch should range from -10 mm to 10 mm
and include only the fringes you would observe. (Label the
locations of the fringes) PLEASE EXPLAIN THOROUGHLY!!!!

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