An X-ray photon of wavelength 0.989 nm strikes a surface. The emitted electron has a kinetic energy of 969 eV. What is the binding energy of the electron in kJ/mol? [KE = 1/2 mv²; 1 electron volt (eV) = 1.602×10^–19 J]

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Hey everyone. And welcome back a photo with a wavelength of 0.3 we two nanometers strikes a surface. The emitted electron has a kinetic energy of 844 electron volts. What is the binding energy of the electron and kilojoules per mole? And we're given four answer choices. A 2.79 multiplied by 10 of the fifth B 5.41 multiplied by 10 of the fifth C 1.22 multiplied by 10 of the fourth and D 3.75 multiplied by 10 to the fourth, all given in kilojoules per mole. So first of all, let's recall that the binding energy can be easily calculated as the difference between the energy of a photon ep and the kinetic energy of that electron ek. Now, what we're going to do here is just express ep which is the energy of a photon as HC divided by a lambda. OK. So we know that and kinetic energy is basically given to us. So in this case, we can say that the binding energy and we have to understand that it is calculated for a single electron because ep the energy of a photon is also calculated or a single photon. So now EB will be the difference between HC divided by Lambda and EK. OK. So we're calculating this difference and if we want to calculate this energy per mole, we actually need to multiply the difference by avocado's number N A because it sells us the energy per mole, right. OK. So we have our formula and we can just substitute everything into that formula. First of all HC we have 6.626 multiplied by 10 to the power of negative 34th joule multiplied by second. This is the planks constant. We multiplied this by the speed of light C 3.00 multiplied by 10 8 m per second. Now, on the bottom, we have to divide this product by lambda which is our wavelength 0.332 nanometers. Let's stick with the si units and convert nanometers into meters knowing that one nanometer is since the negative ninth of a meter. And now we're subtracting the kinetic energy which is 844 electron volts. We need to convert that into jewels because the previous result is given in tools. Now the problem states that one electron volt is 1.602 multiplied by 10 to the negative 19th of a jewel. So we have calculated our, we have calculated our difference and now we need to multiply that by avocado's number 6.022 multiplied by 10 to the power of 23rd mold, the negative first, which clearly shows us that we get per mole or basically tools per mole. And now, since we want to get kilo juice per mole, we need to apply an additional conversion factor. So joules on the bottom kilojoules on top one, kilojoule is 1000 joules. And we have our setup if we calculate the result that we get here, we end up with 2.79 multiplied by 10 to the fifth kilojoules per mole, which corresponds to the answer choice A. That would be it for today. And thank you for watching.

An X-ray photon of wavelength 0.989 nm strikes a surface. The emitted electron has a kinetic energy of 969 eV. What is the binding energy of the electron in kJ/mol? [KE = 1/2 mv²; 1 electron volt (eV) = 1.602×10^–19 J]

Verified Solution

Key Concepts

Photoelectric Effect

Energy of a Photon

Conversion of Energy Units

An X-ray photon of wavelength 0.989 nm strikes a surface. The emitted electron has a kinetic energy of 969 eV. What is the binding energy of the electron in kJ/mol? [KE = 1/2 mv2; 1 electron volt (eV) = 1.602×10–19 J]

Verified Solution

Key Concepts

Photoelectric Effect

Energy of a Photon

Conversion of Energy Units

An X-ray photon of wavelength 0.989 nm strikes a surface. The emitted electron has a kinetic energy of 969 eV. What is the binding energy of the electron in kJ/mol? [KE = 1/2 mv²; 1 electron volt (eV) = 1.602×10^–19 J]