- #1

rwooduk

- 762

- 59

## Homework Statement

## Homework Equations

Please see below.

## The Attempt at a Solution

I'm pretty sure my method is correct but I'm getting small answers:

**$$**

COM \\ \\

E_{6}= E_{2}+E_{\alpha}

\\

\\

Minus \ E_{2} \ and \ square \ both\ sides\\

\\

E_{6}^{2}+E_{2}^{2}-2E_{2}E_{6}=E_{\alpha}^{2}\\ \\

E_{6}^{2}= m_{6}^{2}c^{4}\\

\\

E_{2}^{2}= \rho_{\alpha}^{2}c^{2} + m_{2}^{2}c^{4}\\ \\

E_{\alpha}^{2}= \rho_{\alpha}^{2}c^{2} + m_{\alpha}^{2}c^{4}\\ \\

Rearranging \ I \ get: \\ \\

E_{2}=\frac{(m_{6}^{2}+m_{2}^{2}-m_{\alpha}^{2})c^{4}}{2E_{6}}$$

Now this is where I get strange results (probably my units), if I sub in for $$E_{6}$$ and insert numerical values I get:

COM \\ \\

E_{6}= E_{2}+E_{\alpha}

\\

\\

Minus \ E_{2} \ and \ square \ both\ sides\\

\\

E_{6}^{2}+E_{2}^{2}-2E_{2}E_{6}=E_{\alpha}^{2}\\ \\

E_{6}^{2}= m_{6}^{2}c^{4}\\

\\

E_{2}^{2}= \rho_{\alpha}^{2}c^{2} + m_{2}^{2}c^{4}\\ \\

E_{\alpha}^{2}= \rho_{\alpha}^{2}c^{2} + m_{\alpha}^{2}c^{4}\\ \\

Rearranging \ I \ get: \\ \\

E_{2}=\frac{(m_{6}^{2}+m_{2}^{2}-m_{\alpha}^{2})c^{4}}{2E_{6}}$$

Now this is where I get strange results (probably my units), if I sub in for $$E_{6}$$ and insert numerical values I get:

**$$E_{2}=\frac{(8.71\cdot 10^{10})(\frac{MeV}{c^{2}})^{2}c^{4}}{2\cdot (210541.379)(\frac{MeV}{c^{2}})c^{2}}= \frac{(8.71\cdot 10^{10})(\frac{MeV}{c^{2}})c^{2}}{2\cdot (210541.379)}$$**

Which is 206808MeV. Then if I divide by c^2 I get ~7x10^-4 MeV/c^2 which is really small?