Can anyone help me re-arrange the T.OF Mass spec equations?

d = √(2KE/m) t

What do I do here? The TOF equation is suposed to be t= d x √(m/2KE)
I'm not sure how the equation sudenly flipped and how D is multiplied by the square root?
I would assume it would be D/ √(2KE/m) = t but what do I know im stupid :c

Starting with $d = \sqrt{\frac{2KE}{m}} t$

then making t the subject by dividing both sides by $\sqrt{\frac{2KE}{m}}$

$t = \frac{d}{ \sqrt{\frac{2KE}{m}}}$

You then just turn the fraction upside down and use multiply instead (since dividing by 1/2 is the same as multiplying by 2)

Hiya, thanks for the help but im just confused with this last part.
- why do we turn the fraction upside down and what do we multiply with?

like I dont understand how. Surely t = \frac{d}{ \sqrt{\frac{2KE}{m}}} is the most simplified version? its this part im stuck on :c
Thanks for the help though

Sorry, my latex is a bit rusty!

$t = \frac{d}{ \sqrt{\frac{2KE}{m}}}$ is equivalent to the one that's quoted. It just looks different due to some minor algebraic tweaking.

Specifically, it's been adapted so that it isn't in the ''fraction of a fraction'' type format. You can stick the numbers into both and get the same answer.

Instead of $\frac{x}{1/2}$ (i.e. fraction of a fraction) they've just flipped the 'denominator fraction' so that the two goes onto the top line. So it becomes $\frac{2x}{1} = 2x$

In the question then:

$t = \frac{d}{ \sqrt{\frac{2KE}{m}}} = d\sqrt{\frac{m}{2KE}}[br] [br]$

Ah I see!
Just to confirm like with the example above (X/1/2) can be written as X/1 ÷ 1/2.
We can flip this around to form X/1 x 2/1 giving us 2X/1

However when doing this method with the above answer I get:
______
d/1 ÷ √2ke/m
______
which gives D/1 x √m/2Ke
______
which gives me √Dm/2Ke
_____
Instead of D x √2ke/m

:c

Yep, exactly.



Formatting on TSR isn't great But your mistake appears to be on the line second from bottom. It's wrong to pull the D into the square root, it should be multiplying outside of it:

D/1 x √m/2Ke = D x √m/2Ke not √Dm/2Ke

edit: also why does that racoon in your pic have such a big bum

RIIIIGHT OMG! AHA that great feeling when everything pulls together is so brilliant. Thanks you so much!
I'm so so sorry arghh I haven't done maths since lower school you see and my brain has turned to mush after this long holiday. I was in my second year of A-levels and my exams got cancelled so I have been on holiday for like 3 months now and counting.

Yeah Sorry about the formatting Idk how you managed to pull it off in your replies

and as for the racoon It must have been a picture I pulled off from my faviroute cartoon tv show 'Regular Show' from the character Rigby. I haven't used TSR in a while so I must've done this when I was younger and never bother to change it. The title of my name still stands though!