What is the velocity (in m/s) of an electron that has a wavelength of 3.13 x 10 5 pm? (Mass of an electron = 9.11 x 10 -31 kg).

Here it says, what is the velocity in meters per second of an electron that has a wavelength of 3.13 times 10 to 5 picometers? The mass of an electron is recorded as 9.11 times 10 to the negative 31 kilograms. Alright. So we're gonna have here wavelength equals Planck's constant over mass times velocity. We need to isolate velocity, so let's rearrange this formula. Multiply both sides by mass and velocity, and then we're gonna have mass times velocity times wavelength equals Planck's constant. Let's isolate velocity now. So divide out mass and wavelength, and we'll have velocity isolated. So our new equation becomes velocity equals Planck's constant divided by mass times wavelength. So here, 6.626 times 10 to the negative 34. Remember, Planck's constant is in joules times seconds, and what you need to realize here is that joules is equivalent to kilograms times meter squared over seconds squared. So seconds would cancel out. So units now are kilograms times meter squared over seconds, divide by the mass of the subatomic particle. Wave width needs to be in meters, So we have 3.13 times 10 to the 5 picometers, and we're gonna say here for every 1 picometer it's 10 to the negative 12 meters. So that's 3.13 times 10 to the negative 7 meters. So that's what we're gonna plug in here. So if we look we see what units cancel out. We have kilograms cancel out with kilograms, mass meters cancel out with 1 of the meters, leaving us meters per second. So here this would come out to be, 2320 meters per second. Here our answer has 3 sig figs, because the values given to us in the question also have 3 significant figures.

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9. Quantum Mechanics

De Broglie Wavelength

General Chemistry

9. Quantum Mechanics

De Broglie Wavelength

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Multiple Choice

What is the velocity (in m/s) of an electron that has a wavelength of 3.13 x 10⁵ pm? (Mass of an electron = 9.11 x 10^-31 kg).

1543 m/s

3220 m/s

2320 m/s

3541 m/s

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Verified step by step guidance

First, convert the wavelength from picometers (pm) to meters (m). Since 1 pm = 1 x 10^-12 m, multiply the given wavelength by this conversion factor: 3.13 x 10^5 pm * 1 x 10^-12 m/pm.

Use the de Broglie wavelength formula to relate the wavelength to the velocity of the electron. The formula is: λ = h / (m * v), where λ is the wavelength, h is Planck's constant (6.626 x 10^-34 Js), m is the mass of the electron, and v is the velocity.

Rearrange the de Broglie equation to solve for velocity (v): v = h / (m * λ).

Substitute the known values into the equation: Planck's constant (h = 6.626 x 10^-34 Js), mass of the electron (m = 9.11 x 10^-31 kg), and the converted wavelength in meters.

Calculate the velocity using the rearranged formula. Ensure all units are consistent to obtain the velocity in meters per second (m/s).