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QuestionA photon with a wavelength of 1.53 nm1.53 \mathrm{~nm} emits an electron with 147eV147 \mathrm{eV}. Find the electron's binding energy in J.

Studdy Solution

STEP 1

Assumptions1. The wavelength of the photon is 1.53 nm1.53 \, nm . The kinetic energy of the emitted electron is 147 eV147 \, eV
3. The conversion factor from electron volts to Joules is 1 eV=1.602×10−19 J1 \, eV =1.602 \times10^{-19} \, J
4. The binding energy is the energy required to remove an electron from an atom, which is equal to the energy of the photon minus the kinetic energy of the electron

STEP 2

First, we need to calculate the energy of the photon. The energy of a photon can be calculated using the formulaphoton=hcλ_{photon} = \frac{hc}{\lambda}wherehh is Planck's constant (6.626×10−34 Js6.626 \times10^{-34} \, Js), cc is the speed of light (.00×108 m/s.00 \times10^{8} \, m/s), λ\lambda is the wavelength of the photon

STEP 3

Now, plug in the given values for hh, cc, and λ\lambda to calculate the energy of the photon. Note that the wavelength needs to be converted from nanometers to meters.
photon=(6.626×10−34 Js)×(3.00×108 m/s)1.53×10−9 m_{photon} = \frac{(6.626 \times10^{-34} \, Js) \times (3.00 \times10^{8} \, m/s)}{1.53 \times10^{-9} \, m}

STEP 4

Calculate the energy of the photon.
photon=1.297×10−18 J_{photon} =1.297 \times10^{-18} \, J

STEP 5

Next, we need to convert the kinetic energy of the electron from electron volts to Joules. We can do this by multiplying the kinetic energy by the conversion factor.
kinetic=Kinetic energy×Conversion factor_{kinetic} = Kinetic\, energy \times Conversion\, factor

STEP 6

Now, plug in the given values for the kinetic energy and the conversion factor to calculate the kinetic energy in Joules.
kinetic=147 eV×1.602×10−19 J/eV_{kinetic} =147 \, eV \times1.602 \times10^{-19} \, J/eV

STEP 7

Calculate the kinetic energy of the electron.
kinetic=2.355×10−17 J_{kinetic} =2.355 \times10^{-17} \, J

STEP 8

Now that we have the energy of the photon and the kinetic energy of the electron, we can find the binding energy. The binding energy is the energy of the photon minus the kinetic energy of the electron.
binding=photon−kinetic_{binding} =_{photon} -_{kinetic}

STEP 9

Plug in the values for the energy of the photon and the kinetic energy of the electron to calculate the binding energy.
binding=.297×−18 J−2.355×−17 J_{binding} =.297 \times^{-18} \, J -2.355 \times^{-17} \, J

STEP 10

Calculate the binding energy of the electron.
binding=−2.225×10−17 J_{binding} = -2.225 \times10^{-17} \, JThe binding energy of the electron is −2.225×10−17 J-2.225 \times10^{-17} \, J. The negative sign indicates that energy is required to remove the electron from the atom.

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