Relativistic Energy: Calculate Decay Product Kinetic Energy

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Homework Statement


A radium isotope decays to a radon isotope by emitting an α particle (a helium nucleus) according to the decay scheme 226Ra --> 222Rn + 4He. The masses of the atoms are 226.0254 u (226Ra), 222.0176 u (222Rn), and 4.0026 u (4He). What is the total kinetic energy of the decay products (in MeV)?

Homework Equations


E0=mc2
E=gamma*mc2
K=gamma*mc2-mc2
E=K+E0
1u=931.494 (MeV)/c2

The Attempt at a Solution


I really don't know what to do for this...
 
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Please help!
This concept is confusing for me and once I understand this, it will make the rest of my problems much easier to solve.
 
well...how much more massive is the input (radium), than the output (Radon and a Helium nucleus)...I'm not sure if you are confused by the notation, the 4He should be one helium nucleus with 4 nucleons.

~Lyuokdea
 
Aeighme said:
Please help!
This concept is confusing for me and once I understand this, it will make the rest of my problems much easier to solve.

calm down, wait more than 13minutes before bumping thread :-)
 
<< complete solution deleted by berkeman >>
 
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Hi, I had an exam and I completely messed up a problem. Especially one part which was necessary for the rest of the problem. Basically, I have a wormhole metric: $$(ds)^2 = -(dt)^2 + (dr)^2 + (r^2 + b^2)( (d\theta)^2 + sin^2 \theta (d\phi)^2 )$$ Where ##b=1## with an orbit only in the equatorial plane. We also know from the question that the orbit must satisfy this relationship: $$\varepsilon = \frac{1}{2} (\frac{dr}{d\tau})^2 + V_{eff}(r)$$ Ultimately, I was tasked to find the initial...
The value of H equals ## 10^{3}## in natural units, According to : https://en.wikipedia.org/wiki/Natural_units, ## t \sim 10^{-21} sec = 10^{21} Hz ##, and since ## \text{GeV} \sim 10^{24} \text{Hz } ##, ## GeV \sim 10^{24} \times 10^{-21} = 10^3 ## in natural units. So is this conversion correct? Also in the above formula, can I convert H to that natural units , since it’s a constant, while keeping k in Hz ?

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