Estimate Min. Electron Energy in Hydrogen Atom w/ Uncertainty Principle

[asdf1]

for the following question:
a hydorgen atom is 5.3*10^(-11) m in radius. use the uncertainty principle to estimate the minimum energy an electron acan have in this atom.

my problem:
to calculate the kinetic energy, do you use Ek=(p^2)/2m or Ek=pc?

 

[El Hombre Invisible]

The uncertainty principal is: /\x/\p = h/2*pi.

/\x is the radius you have stated.

/\p is the uncertainty of momentum. p = mv, mass is known, so /\p = m/\v.

So: /\v = h/(2 * pi * m * /\x)

where m is the mass of the electron.

Find /\v, then you can find the minimum energy:

energy = 0.5 * m * /\v^2.

 

[asdf1]

is that the same as just calculating the kinetic energy=p^2/2m?

 

[El Hombre Invisible]

Yep, that's another way.

 

[asdf1]

ok~ that's cool!