Comparing the KE of Alpha and Beta particles

[Hemanta]

Homework Statement

If the speed of an alpha particle is 0.5 VB- how does its kinetic energy compare to the kinetic energy of the beta-minus particle?

Relevant Equations

KE = 1/2 mv^2

I try solving it but the answer didn’t match

 

[phinds]

You are asking people for help by posting a dimly lit SIDEWAYS figure? This is why the rules say that your efforts should be typed, not posted as an image.

 

[Hemanta]

You are asking people for help by posting a dimly lit SIDEWAYS figure? This is why the rules say that your efforts should be typed, not posted as an image.

I type too

 

[jbriggs444]

I type too

You could have transcribed the image for us then.

As I make it out, you start with the given from the problem:
$$v_\alpha = 0.5 v_\beta$$
You write down formulas for the kinetic energy of the alpha and for the beta.
$$K_\alpha=\frac{1}{2}m_\alpha v_\alpha^2$$ $$K_\beta=\frac{1}{2}m_\beta v_\beta^2$$
You write a scribble that looks like you want to substitute $(0.5v_\beta)$ in for $v_\alpha$

You evaluate $$\frac{K_\alpha}{K_\beta}$$
cancelling terms wildly (work not shown) you appear to end up with everything canceled except for $0.5^2$ and decide that $$0.5^2 = 0.125$$
In addition to that arithmetic error, you have canceled two terms that do not cancel.

Ideally, you would have included at least one more equation in your work:$$\frac{K_\alpha}{K_\beta}=\frac{ \frac{1}{2}m_\alpha (0.5 v_\beta)^2}{ \frac{1}{2}m_\beta v_\beta^2}$$ With that equation cleanly written, the cancellation of terms is easy to do and hard to do wrong.

 

[phinds]

See, @Hemanta, THAT is what I mean by typing.