How Do You Calculate Wavelength and Recoil Velocity in Nuclear Physics Problems?

[suspecteg]

Homework Statement

hey, 2 questions thanks:
1.A gamma ray is converted to an electron and a positron. If 50% of the gamma ray energy becomes kinetic energy, what is the wavelength of the gamma ray?

2.A nucleus of a radioactive element (mass 10^-25) loses 10^-26g during gamma decay. if the gamma ray has a wavelength of 10^-14m, what is the recoil velocity of the nucleus?

Homework Equations

no idea, we haven't learned about wavelength at all.. however these two questions were in a big revision booklet so id rather be safe than sorry.

The Attempt at a Solution

thanks.

 

[stanton]

You looks like you are just throwing question insincerely to board us to answer. Try to write more carful next time. If you show your attempt, I will tell you the answer. And If you haven't learn it, don't worry. You will be perfectly safe.

 

[kerimek]

Hello, thank you for your questions. As a scientist, it is important to always be prepared for any test or question, so it is great that you are taking the initiative to review material before your test tomorrow.

To answer your first question, we can use the equation E=hc/λ, where E is the energy of the gamma ray, h is Planck's constant, c is the speed of light, and λ is the wavelength. Since 50% of the gamma ray energy becomes kinetic energy, we can set up the equation E/2=1/2mv^2, where m is the mass of the electron and positron and v is their velocity. We can solve for v and plug it into the first equation to solve for λ.

For the second question, we can use the equation mv=hf, where m is the mass of the nucleus, v is the recoil velocity, h is Planck's constant, and f is the frequency of the gamma ray. We can solve for v and plug in the given values to find the recoil velocity of the nucleus.

I understand that you may not have learned about these equations specifically, but they are important concepts in nuclear physics. It would be beneficial to review these equations and their applications in order to better understand these questions and be prepared for your test tomorrow. Best of luck!