Final answer:
The work function of a metal is the minimum energy needed to remove an electron from the surface of the metal. The cutoff frequency of a surface is the minimum frequency of light required to emit electrons from the surface. To find the work function and cutoff frequency, we can use the equations relating them to each other and other known values.
Step-by-step explanation:
The work function of a metal is the minimum energy needed to remove an electron from the surface of the metal. It is represented by the symbol Φ. The cutoff frequency of a surface is the minimum frequency of light required to emit electrons from the surface. It is related to the work function by the equation:
fcutoff = (Φ / h) x c
where fcutoff is the cutoff frequency, Φ is the work function, h is Planck's constant (6.626 x 10^-34 J s), and c is the speed of light (3.00 x 10^8 m/s).
To find the work function, we can rearrange the equation and solve for Φ:
Φ = (fcutoff x h) / c
Using the given wavelength of 400 nm (or 4.00 x 10^-7 m), we can convert it to frequency using the equation:
f = c / λ
Substituting the values into the equation, we can calculate the cutoff frequency:
fcutoff = (3.00 x 10^8 m/s) / (4.00 x 10^-7 m) = 7.50 x 10^14 Hz
Finally, substituting the values into the rearranged equation, we can calculate the work function:
Φ = (7.50 x 10^14 Hz x 6.626 x 10^-34 J s) / (3.00 x 10^8 m/s) = 1.66 x 10^-19 J