When light of wavelength 130 nm falls on a cobalt surface, electrons having a maximum kinetic energy of 4.55 eV are emitted. Find values for the following.
(a) the work function of cobalt (in eV)
(b) the cutoff wavelength (in nm)
(c) the frequency corresponding to the cutoff wavelength (in Hz)
KE emitted=workfunction+incomingenergy
incomingenergy= Plancksconstant(c/lambda)
solve for work function
cutoff wavlength
c/lambdacutoff= work function
To find the values for the questions, we can use the following equations:
(a) The work function (Φ) is the minimum amount of energy required to remove an electron from the surface of a material. We can use the equation:
Energy of incident photon = Work function + Maximum kinetic energy of emitted electron
Given:
Wavelength of incident light (λ) = 130 nm
Maximum kinetic energy of emitted electron (KEmax) = 4.55 eV
To convert the wavelength to energy, we can use the equation:
Energy of photon = (hc) / λ
where h is Planck's constant (6.626 x 10^-34 J.s) and c is the speed of light (3 x 10^8 m/s).
Converting the given wavelength to meters:
λ = 130 nm = 130 x 10^-9 m
Calculating the energy of the photon:
Energy of photon = (6.626 x 10^-34 J.s)(3 x 10^8 m/s) / (130 x 10^-9 m)
Now, we need to convert the energy of the photon to electron volts (eV). Since 1 eV is equal to 1.602 x 10^-19 J, we can use this conversion factor.
Energy of photon (in eV) = Energy of photon (in J) / (1.602 x 10^-19 J/eV)
Now, we can write the equation:
Energy of photon (in eV) = [(6.626 x 10^-34 J.s)(3 x 10^8 m/s) / (130 x 10^-9 m)] / (1.602 x 10^-19 J/eV)
Substituting the values and solving the equation will give us the energy of the photon in eV.
(b) The cutoff wavelength (λc) is the maximum wavelength (in nm) of light that can cause photoemission. It is given by:
λc = (hc) / Φ
where Φ is the work function.
Rearranging the equation, we have:
Φ = (hc) / λc
We can use the same values for h and c as before, and substitute the cutoff wavelength to find the work function.
(c) The frequency corresponding to the cutoff wavelength can be found using the equation:
f = c / λc
where c is the speed of light and λc is the cutoff wavelength.
Calculating f using the given values will give us the frequency corresponding to the cutoff wavelength.
By using these equations and substituting the given values, we can find the values for (a) the work function, (b) the cutoff wavelength, and (c) the frequency corresponding to the cutoff wavelength.