A-level electron speed question

[felix-corpus]

calculate the speed of an electon which has a de broglie wave length of 1.3x10^-10m


can anyone help me with this question I've never had one like this come up so i haven't a clue what to do, with only 2 weeks to my a-level exams

 

[Fightfish]

Have you come across the de Broglie relation
[tex]\lambda = \frac{h}{p}[/tex]
for matter waves?

 

[kerimek]

Sure, I can help you with this question. First, let's review some important concepts. The de Broglie wavelength is a concept in quantum mechanics that relates the momentum of a particle to its wavelength. It is given by the formula λ = h/p, where λ is the de Broglie wavelength, h is Planck's constant, and p is the momentum of the particle.

In this question, we are given the de Broglie wavelength (1.3x10^-10m) and we need to calculate the speed of the electron. To do this, we will use the formula for momentum, p = mv, where m is the mass of the electron and v is its speed.

Now, the mass of an electron is approximately 9.11x10^-31 kg. Plugging this into the formula for momentum, we get p = (9.11x10^-31 kg)v. We can rearrange this equation to solve for v, the speed of the electron.

v = p/(9.11x10^-31 kg)

But we still need to find the value of p, the momentum. To do this, we can use the formula for de Broglie wavelength, λ = h/p, and rearrange it to solve for p.

p = h/λ

Now, we can plug in the given values for h (6.63x10^-34 J·s) and λ (1.3x10^-10m) to get the momentum of the electron.

p = (6.63x10^-34 J·s)/(1.3x10^-10m) = 5.10x10^-25 kg·m/s

Finally, we can substitute this value of p into our equation for speed to get the final answer.

v = (5.10x10^-25 kg·m/s)/(9.11x10^-31 kg) = 5.59x10^6 m/s

Therefore, the speed of the electron with a de Broglie wavelength of 1.3x10^-10m is approximately 5.59x10^6 m/s. I hope this helps you understand how to approach this type of question. Good luck on your exams!