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Chapter 36: Problem 28

The threshold wavelength for the photoelectric effect in a specific alloy is \(400 . \mathrm{nm}\). What is the work function in \(\mathrm{eV} ?\)

Short Answer

Expert verified
Answer: The work function of the alloy is 3.1 eV.

Step by step solution

01

Identify given information and constants

The information provided by the exercise is: - Threshold wavelength (\(λ_{threshold}\)) = 400 nm - Planck's constant (\(h\)) = 6.626 x 10^-34 Js - Speed of light (\(c\)) = 3 x 10^8 m/s - Electron charge (\(e\)) = 1.602 x 10^-19 C
02

Convert the threshold wavelength to meters

To work with the threshold wavelength in the equations, we need to have it in meters. So, we will convert the wavelength from nm to meters: \(λ_{threshold} = 400\,\text{nm} \times \frac{1\,\text{m}}{10^9\,\text{nm}} = 4 \times 10^{-7}\,\text{m}\)
03

Calculate the energy when electrons are ejected

Now, we can use Planck's equation to find the energy (\(E\)) needed to eject electrons as: \(E = \frac{h \times c}{λ_{threshold}}\) Substitute the known values into the equation: \(E = \frac{(6.626 \times 10^{-34}\,\text{Js}) \times (3 \times 10^8\,\text{m/s})}{(4 \times 10^{-7}\,\text{m})} = 4.9695 \times 10^{-19}\,\text{J}\)
04

Convert the energy into electron volts

To find the energy in electron volts (eV), we will divide the energy in joules by the electron charge: \(E_{eV} = \frac{E}{e} = \frac{4.9695 \times 10^{-19}\,\text{J}}{1.602 \times 10^{-19}\,\text{C}} = 3.1\,\text{eV}\)
05

Find the work function

The work function is the minimum energy required to eject electrons, and in this case, it is equal to the calculated energy in electron volts: Work function = \(E_{eV} = 3.1\,\text{eV}\) Hence, the work function of the specific alloy is \(3.1\,\text{eV}\).

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Most popular questions from this chapter

Now consider de Broglie waves for a (relativistic) particle of mass \(m\), momentum \(p=m v \gamma\), and total energy \(E=m c^{2} \gamma\), with \(\gamma=\left[1-(v / c)^{2}\right]^{-1 / 2}\). The waves have wavelength \(\lambda=h / p\) and frequency \(f=E / h\) as before, but with the relativistic momentum and energy. a) Calculate the dispersion relation for these waves. b) Calculate the phase and group velocities of these waves. Now which corresponds to the classical velocity of the particle?

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