Calculating Recoil Velocity of Cobalt-60 Nucleus Emitted Gamma Ray

[Astronomer186]

A radioactive nucelus (cobalt - 60, has 27 p+'s and 33 e-'s) emits a photon (gamma ray) of wavelength 2.7 x 10^-13 m. Assuming the nucleus was intially at rest, what si its recoil velocity upon emitting this photon?

I have already figured out the momentum using this information. When I looked at the solution guide of how to find the mass, I am not sure why they use:

m = 60(1.67 x 10^-27 kg)?

to figure out the mass? I mean, I can understand the number 60, because that's the atomic mass, but why multiply it by the mass of a proton? Cobalt has two charges: 2+ and 3+. The most common one is 2+, so why multiply it by the mass of a proton, rather than an alpha particle (which has a 2+ charge)?

If someone can explain this, that would be greatly appreciated, because I am so confused. Thank you.

 

[Tide]

You're talking about the mass of a cobalt nucleus and not the charge. Cobalt 60 has 60 nucleons and there is little difference between the masses of protons and neutrons.

 

[quicknote]

I would like to explain the reasoning behind using the mass of a proton in this calculation. First, it is important to note that the charge of an atom or nucleus does not determine its mass. The mass of an atom or nucleus is primarily determined by the number of protons and neutrons it contains. In the case of cobalt-60, it has 27 protons and 33 neutrons, giving it a mass number of 60.

The reason why we use the mass of a proton in this calculation is because the recoil velocity of the cobalt-60 nucleus is directly related to its mass. The equation for calculating recoil velocity is given by v = p/m, where v is the recoil velocity, p is the momentum, and m is the mass. In order to use this equation, we need to have the mass of the cobalt-60 nucleus in kilograms.

Now, the mass of an individual proton is very small (approximately 1.67 x 10^-27 kg), but when we multiply it by the total number of protons in the cobalt-60 nucleus (27), we get a more significant value (approximately 4.5 x 10^-26 kg). This is the mass of the cobalt-60 nucleus that we need to use in our calculation.

In summary, we use the mass of a proton in this calculation because it helps us determine the mass of the cobalt-60 nucleus, which is essential in calculating the recoil velocity. I hope this explanation helps to clarify any confusion you may have had.