Answer with Explanation:
We are given that
Threshold wavelength,[tex]\lambda_0=262 nm=262\times 10^{-9} m[/tex]
[tex]1 nm=10^{-9} m[/tex]
a.Work function,[tex]w_0=\frac{hc}{\lambda_0}[/tex]
Where [tex]h=6.626\times 10^{-34}[/tex]
[tex]c=3\times 10^8 m/s[/tex]
Using the formula
[tex]w_0=\frac{6.626\times 10^{-34}\times 3\times 10^8}{262\times 10^{-9}}[/tex]
[tex]w_0=7.59\times 10^{-19} J[/tex]
b.Wavelength,[tex]\lambda=222nm=222\times 10^{-9} m[/tex]
[tex]K.E=\frac{hc}{\lambda}-7.59\times 10^{-19}[/tex]
[tex]K.E=\frac{6.626\times 10^{-34}\times 3\times 10^8}{222\times 10^{-9}}-7.59\times 10^{-19}[/tex]
[tex]K.E=8.95\times 10^{-19}-7.59\times 10^{-19}=1.36\times 10^{-19} J[/tex]
Hence, the maximum kinetic energy of an electron emitted=[tex]1.36\times 10^{-19} J[/tex]
a. The work function for silver is equal to 4.73 eV.
b. The maximum kinetic energy of an electron emitted from silver is [tex]1.38 \times 10^{-19}\;Joules[/tex].
Given the following data:
a. To find the work function for silver, we would use Einstein's equation for photon energy:
Mathematically, Einstein's equation for photon energy is given by the formula:
[tex]E = hf = h\frac{v}{\lambda}[/tex]
Where:
When the maximum kinetic energy of an electron is equal to zero (0), the work function of the electron is given by:
[tex]\phi = \frac{hv}{\lambda_t}[/tex]
h = [tex]6.626 \times 10^{-34}\;J.s = 4.136 \times 10^{-15} \;eV.s[/tex]
Substituting the given parameters into the formula, we have;
[tex]\phi = \frac{4.136 \times 10^{-15} \times 3.0 \times 10^{8}}{262}\\\\\phi = \frac{1240}{262}[/tex]
Work function, [tex]\phi[/tex] = 4.73 eV
b. To find the maximum kinetic energy of an electron emitted from silver, if the incident light has a wavelength of 222 nm:
[tex]K.E_{max} = \frac{hc}{\lambda} - \phi\\\\K.E_{max} = \frac{4.136 \times 10^{-15} \times 3.0 \times 10^{8}}{222} - 4.73\\\\K.E_{max} = \frac{1240}{222} - 4.73\\\\K.E_{max} = 5.59 - 4.73\\\\K.E_{max} = 0.86\;eV[/tex]
[tex]1 \;eV = 1.602 \times 10^{-19}\;J[/tex]
[tex]0.86 \;eV = 0.86 \times1.602 \times 10^{-19}\;J\\\\0.86 \;eV = 1.38 \times 10^{-19}\;Joules[/tex]
Maximum kinetic energy = [tex]1.38 \times 10^{-19}\;Joules[/tex]
Read more: https://brainly.com/question/16901506
