As you may well know, placing metal objects inside a microwave oven can generate sparks. Two of your friends are arguing over the cause of the sparking, with one stating that the microwaves "herd" electrons into "pointy" areas of the metal object, from which the electrons jump from one part of the object to another. The other friend says that the sparks are caused by the photoelectric effect. In this problem, we will prove or disprove the latter idea using basic physics. Suppose the typical work function of the metal is roughly 3.340 × 10-19 J. Calculate the maximum wavelength in angstroms of the radiation that will eject electrons from the metal.

work function = hc/wavelength

3.340E-19 = hc/wavelength
Solve for wavelength. I get approx 600 nm

no

To calculate the maximum wavelength of the radiation that will eject electrons from the metal, we can use the equation for the photoelectric effect:

E = hf

Where:
E is the energy required to eject an electron from the metal surface (equal to the work function),
h is Planck's constant (6.626 × 10^-34 J·s), and
f is the frequency of the radiation.

Since we are asked to calculate the maximum wavelength, we need to find the minimum frequency of the radiation. This can be achieved by rearranging the equation:

E = hf
f = E / h

Substituting the given work function (3.340 × 10^-19 J) and Planck's constant, we can solve for the frequency:

f = (3.340 × 10^-19 J) / (6.626 × 10^-34 J·s)
f ≈ 5.044 × 10^14 Hz

Now, we can use the equation c = λf (where c is the speed of light and λ is the wavelength) to find the maximum wavelength:

c = λf
λ = c / f

Substituting the speed of light (2.998 × 10^8 m/s) and the frequency we found earlier:

λ = (2.998 × 10^8 m/s) / (5.044 × 10^14 Hz)
λ ≈ 5.94 × 10^-7 m

Converting the wavelength from meters to angstroms:

λ ≈ 5.94 × 10^-7 m * (1 × 10^10 Å/m)
λ ≈ 5.94 × 10^3 Å

Therefore, the maximum wavelength of the radiation that will eject electrons from the metal is approximately 5.94 × 10^3 angstroms.

To determine the maximum wavelength of radiation that will eject electrons from the metal using the photoelectric effect, we can make use of Einstein's photoelectric equation:

E = hf = Φ + K.E.

Where:
E is the energy of a photon,
h is Planck's constant (6.626 × 10^-34 J·s),
f is the frequency of the radiation,
Φ is the work function of the metal (3.340 × 10^-19 J),
and K.E. is the kinetic energy of the ejected electron.

Since we want to calculate the maximum wavelength, we need to find the minimum energy required to eject an electron, which occurs when all the energy is used to overcome the work function (i.e., K.E. = 0).

In this case, the equation becomes:

E = hf = Φ

We can rearrange this equation to solve for the frequency:

f = Φ / h

Now, we can use the relationship between frequency and wavelength:

c = fλ

Where c is the speed of light (2.998 × 10^8 m/s), and λ is the wavelength.

Rearranging to solve for wavelength:

λ = c / f

Substituting the value of frequency (f = Φ / h) into the equation:

λ = c / (Φ / h)

Let's plug in the given values:

λ = (2.998 × 10^8 m/s) / ((3.340 × 10^-19 J) / (6.626 × 10^-34 J·s))

Simplifying:

λ = (2.998 × 10^8 m/s) × ((6.626 × 10^-34 J·s) / (3.340 × 10^-19 J))

λ = (2.998 × 10^8 m/s) × (6.626 × 10^-34 J·s) / (3.340 × 10^-19 J)

Calculating:

λ ≈ 5.965 × 10^-7 m

To convert this wavelength to angstroms, we can multiply by 10^10:

λ ≈ 5.965 × 10^-7 m * 10^10 Angstroms/m

λ ≈ 5965 Angstroms

Therefore, the maximum wavelength of radiation that will eject electrons from the metal, based on the given work function, is approximately 5965 Angstroms.