Question

Electrons are accelerated by 2150V in an electron microscope.

What is the maximum possible resolution?

(Answer in meters)

Please show all work.

Answer 1

We know

$\lambda =\frac{h}{p}$       (De-Brogle equation) p is momentum and h is plank constant.

we also have P= $\sqrt{2mE}$     ( here m is mass and E is energy )

from above both eqution      

$\lambda =\frac{h}{\sqrt{2mE}}$      ---------------------------------------------------(1)

also E=qV ( q charge and V is voltage)

putting value of E in eq 1

$\lambda =\frac{h}{\sqrt{2mqV}}$      (This is the equation for maximum resolution)

putting values of h=6.62 $\times 10^{^{-34}}$ , m=9.1 $\times$ 10^-31kg, q=1.6 $\times$ 10^-19 c, V=2150v

$\lambda =\frac{6.62\times 10^{-34}}{\sqrt{2\times 9.1\times 10^{-31}\times 1.6\times 10^{-19}\times 2150}}$       =2.64 $\times$ 10¹⁴ meter (ans)