Chapter 6: Problem 65

Estimate the binding energy of electrons in bolocis magnesium, given that the wavelength of \(337 \mathrm{nm}\) is the longest wavelength that a photon may have to eject a photoelectron from magnesium photoelectrode.

Short Answer

Expert verified

The binding energy of electrons in magnesium can be estimated using the given wavelength of \(337 \mathrm{nm}\) and the energy of a photon equation \(E = h\frac{c}{\lambda}\). After converting the wavelength to meters, calculating the energy in Joules, and converting to electron volts, we find that the binding energy of electrons in magnesium is approximately \(3.66 eV\).

Step by step solution

Write down the equation for energy of a photon

The energy of a photon can be calculated using the equation: \(E = h\frac{c}{\lambda}\) Where: - \(E\) is the energy of the photon - \(h\) is the Planck's constant (\(6.626 \times 10^{-34} J\cdot s\)) - \(c\) is the speed of light in vacuum (\(3 \times 10^8 m/s\)) - \(\lambda\) is the wavelength of the photon

Substitute the given values into the equation

The wavelength \(\lambda\) is given as \(337 \mathrm{nm}\). We need to convert this into meters for our equation. The conversion factor is \(1 \mathrm{nm} = 10^{-9} m\). So, \(\lambda = 337 \times 10^{-9} m\). Now, substitute the values into the equation: \(E = (6.626 \times 10^{-34} J\cdot s) \frac{3 \times 10^8 m/s}{337 \times 10^{-9} m}\)

Calculate the energy of the photon

Now, calculate the energy of the photon: \(E = (6.626 \times 10^{-34} J\cdot s) \frac{3 \times 10^8 m/s}{337 \times 10^{-9} m} \approx 5.87 \times 10^{-19} J\)

Convert the energy from joules to electron volts

To convert the energy from joules to electron volts, use the relationship \(1 eV = 1.602 \times 10^{-19} J\). Divide the energy in joules by the conversion factor to get the energy in electron volts: \(E_{eV} = \frac{5.87 \times 10^{-19} J}{1.602 \times 10^{-19} J/eV} \approx 3.66 eV\)

State the binding energy of the electrons in magnesium

The binding energy of electrons in magnesium is approximately \(3.66 eV\).

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Estimate the binding energy of electrons in bolocis magnesium, given that the wavelength of \(337 \mathrm{nm}\) is the longest wavelength that a photon may have to eject a photoelectron from magnesium photoelectrode.

Short Answer

Step by step solution

Write down the equation for energy of a photon

Substitute the given values into the equation

Calculate the energy of the photon

Convert the energy from joules to electron volts

State the binding energy of the electrons in magnesium

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