How Do You Calculate the Work Function of Metal in Quantum Physics?

[Charlie Brown]

An incident radiation has a wavelength of 42.86 nm and is consequently enough to eject electrons through a retarding potential of 20.95 volts, so that they end up with a velocity of exactly 6.00 X 10^5 m/s. Calculate the work function of the particular metal. (Answer id electron volts)

 

[Nylex]

Do you have any ideas about what equation to use?

 

[thepatientmental]

To calculate the work function, we can use the equation:

Kmax = eV0 = h(f-f0)

where Kmax is the maximum kinetic energy of the ejected electrons, e is the charge of an electron, V0 is the retarding potential, h is Planck's constant, f is the frequency of the incident radiation, and f0 is the threshold frequency (corresponding to the work function).

We are given the values for Kmax (calculated from the given velocity), V0, and f (converted from the given wavelength). So, we can rearrange the equation to solve for f0:

f0 = f - (Kmax/e)/h

Plugging in the values, we get:

f0 = (3.00 X 10^8 m/s) / (42.86 X 10^-9 m) - (6.00 X 10^5 m/s)^2 / (9.11 X 10^-31 kg)(1.60 X 10^-19 C)(6.63 X 10^-34 J*s)

= 6.99 X 10^14 Hz

Now, we can use the equation:

f0 = c / λ0

where c is the speed of light and λ0 is the threshold wavelength.

Solving for λ0, we get:

λ0 = c / f0 = (3.00 X 10^8 m/s) / (6.99 X 10^14 Hz) = 4.29 X 10^-7 m = 429 nm

Finally, to calculate the work function, we can use the equation:

Φ = hc / λ0

where Φ is the work function, h is Planck's constant, c is the speed of light, and λ0 is the threshold wavelength.

Plugging in the values, we get:

Φ = (6.63 X 10^-34 J*s)(3.00 X 10^8 m/s) / (429 X 10^-9 m) = 4.63 X 10^-19 J = 4.63 eV

Therefore, the work function of the metal is 4.63 electron volts.