Energy equivalent of 10^-18 cm extra dimension

[moriheru]

I am actually quite sure I have it right but my book would then be wrong so I have posted my problem here to see if I didn't do a embarassing mistake in arithmetics.

Homework Statement

"Show that the energy equivalent of the length 10^-18cm of a large extra dimension is roughly 20TeV"
-Zwiebach 2004

2. Homework Equations
ħ=c=1
ħc≈200MeVx10^-15m
l_s=√α
mc²=ħc/ l

The Attempt at a Solution

Just some simple reforming first:

E=mc²=ħc/l

then substituting numbers and converting units:

10^-18cm=10^-16m

E=200MeVx10^-15 m / 10^-16 m

= 200 MeVx10x10

=20000 MeV=2x10¹⁰ eV

,where Zwiebach says it schould be roughly 20 Tev 10^12 eV.

Thanks for any clarifiactions

 

[Orodruin]

10-18cm=10-16m

Is 0.01 cm = 1 m?

 

[moriheru]

I see.