De Broglie and other Quantum Questions

[DizzyDoo]

Hi, just some quantum physics questions. I've given them all a good go, the first two just require checking, but the rest I'm rather stuck on. They're the last questions in about 20 other ones, and my head now hurts. :(

Any hints are very much appreciated!

Homework Statement

17. Metal X has a work function of 5.0 eV and is used in a demonstration of the photoelectric effect.
a) What is the min. frequency needed to remove electrons from X?

I firstly got converted the 5eV to joules which gave m 8 x 10^-19. I then divided that by the Planck's constant to get my final answer of 1.21 x 10¹⁵Hz

b) What is the wavelength of these waves?

I got the wavelength of 2.49 x 10^-7, by dividing the speed of an EM wave by the answer to A.

c) If metal X was irradiated with EM waves of frequency 2.0 x 1015 Hz, what will be the maximum kinetic energy of the photoelectrons released?

I'm afraid this is where I get stuck. The possible equations that I know are KE = 0.5mv² and hf = φ + ½ mv²_max but here I am unsure of the theory. :(

18. In the following two situations, calculate the de Broglie wavelength and, hence, state whether the particle or the wave model should be used.
a) Neutrons (m=1.8x10^-28kg) moving at 107ms^-1 passing a gap of 8x10^-10m

Pretty sure this is the particle model. Unsure of how to calculate the wavelength though, any ideas?

b) Electrons with a momentum of 4x10^-19kgms-1 passing nuclei diameter 10^-15m

I'm pretty sure this is the wave model. Same as the previous question.

Thanks for reading!

 

[dx]

17 c: If you supply energy hf to the electron, and W of this energy is used up to remove it from the metal, how much of the energy is left as kinetic energy?

18 a: The de Broglie wavelength is given by p = h/λ.

 

[nlightner]

Hi there, it's great to see that you are actively engaged in your quantum physics studies! I can understand how these last few questions may be causing some confusion and frustration, but don't worry, I'm here to help.

For question 17a, your method of converting the work function to joules and then dividing by Planck's constant is correct. Your answer of 1.21 x 10^15 Hz is also correct. Well done!

For question 17b, you are on the right track with dividing the speed of an EM wave by the frequency from part a. However, you need to remember to use the equation c = λν, where c is the speed of light, λ is the wavelength, and ν is the frequency. Rearranging this equation for λ will give you the correct wavelength of 1.5 x 10^-7 m.

Moving on to question 17c, you are on the right track with the equations you listed. However, you need to use the equation KE = hf - φ, where KE is the kinetic energy of the photoelectrons, h is Planck's constant, f is the frequency of the EM waves, and φ is the work function. Plugging in the given values, you will get a maximum kinetic energy of 3.8 x 10^-19 J.

For question 18a, you are correct that this situation requires the particle model. To calculate the de Broglie wavelength, you can use the equation λ = h/p, where λ is the wavelength, h is Planck's constant, and p is the momentum of the particle. Plugging in the given values, you will get a de Broglie wavelength of 4.1 x 10^-15 m.

Finally, for question 18b, you are correct that this situation requires the wave model. To calculate the de Broglie wavelength, you can use the equation λ = h/mv, where λ is the wavelength, h is Planck's constant, m is the mass of the electron, and v is its velocity. Plugging in the given values, you will get a de Broglie wavelength of 3.3 x 10^-10 m.

I hope this helps clear up any confusion and gives you a better understanding of these concepts. Keep up the good work and don't hesitate to ask for help when needed. Best of luck