##### physics question 1 hw 20

 Physics Tutor: None Selected Time limit: 1 Day

1. When light of wavelength 322 nm falls on a potassium surface, electrons are emitted that have a maximum kinetic energy of 1.35 eV. What is the work function of potassium? The speed of light is 3 × 108 m/s and Planck’s constant is 6.63 × 10−34 J · s. Answer in units of eV.

2. What is the cutoff wavelength of potassium? Answer in units of nm.

3.What is the threshold frequency for potassium? Answer in units of Hz.

Jul 15th, 2015

$\\ \lambda=322\hspace{5}nm=322\times10^{-9}\hspace{5}nm\\ \\ K_{max}=1.35\hspace{5}eV\\ \\ h=6.63\times10^{-34}\hspace{5}Js=\frac{6.63\times10^{-34}\hspace{5}Js}{1.6\times10^{-19}\hspace{5}J/ev}=4.13\times10^{-15}\hspace{5}eVs\\ \\$

$\lambda=322\hspace{5}nm=322\times10^{-9}\hspace{5}m$

According to Einstein's photoelectric equation

$\\ h\upsilon =\phi +K_{max}\\$

where $\\ \phi$ is the work function.

$\\ \phi=h\upsilon-K_{max}\\ \\ \phi=\frac{hc}{\lambda}-K_{max}\\ \\ \phi=\frac{4.13\times10^{-15}\hspace{5}eVs\times3\times10^8\hspace{5}m/s}{322\times10^{-9}\hspace{5}m}-1.35\hspace{5}eV\\ \\ \phi=3.85\hspace{5}eV-1.35\hspace{5}eV\\ \\ \phi=2.5\hspace{5}eV$

Jul 15th, 2015

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Jul 15th, 2015

To find the cutoff wavelength, equate the energy of incident light and the work function.

$\\ h\upsilon_{\circ}=\phi\\ \\ \frac{hc}{\lambda_{\circ}}=\phi\\ \\ \lambda_{\circ}=\frac{hc}{\phi}\\ \\ \lambda_{\circ}=\frac{4.13\times10^{-15}\hspace{5}eVs\times3\times10^8\hspace{5}m/s}{2.5\hspace{5}eV}\\ \\ \lambda_{\circ}=4.956\times10^{-7}\hspace{5}m\\ \\ \lambda_{\circ}=495.6\times10^{-9}\hspace{5}m\\ \\ \lambda_{\circ}=495.6\hspace{5}nm\\$

This is the cutoff wavelength.

Threshold frequency is

$\\ \upsilon_{\circ}=\frac{c}{\lambda_{\circ}}\\ \\ \upsilon_{\circ}=\frac{3\times10^8\hspace{5}m/s}{4.956\times10^{-7}\hspace{5}m}\\ \\ \upsilon_{\circ}=6.05\times10^{14}\hspace{5}Hz$

If the frequency of light falls below threshold frequency then no electrons will be emitted.

Jul 15th, 2015

Sorry for the delay.

Jul 15th, 2015

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Jul 15th, 2015
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Jul 15th, 2015
Dec 9th, 2016
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