calculate the uncertainity in the position of an electron if the uncertainity in its velocity is 5 7*10 to the - Chemistry -

Question

calculate the uncertainity in the position of an electron if the
uncertainity in its velocity is 5 7*10 to the power 5 m/s(h=6 6*10
to the power -34js and m=9 1*10 to the power -31 kg)

Shubhangini Kumari · Accepted Answer

Dear student!

We know that, uncertainty is derived
as;

Î”x Î”p = h/
4Ï€ where, Î”x is uncertainty in position and
Î”p is uncertainty in momentum,

Now we know that Î”p = m
Î”v

Hence, putting the value we can get
uncertainty in position as;

Î”x mÎ”v = h
/4Ï€

or, Î”x = h / (4Ï€ m
Î”v)

Here, Î”v =5 7 x 105
m/s and mass of electron, m =9 1x 10-31
kg

So, Î”x = h / 4Ï€ m
Î”v

Î”x = 6 6 x 10-34 / 4
x 22/7 x 9 1x 10-31x 5 7 x 105 = 1x
10-10 m

or, Î”x =
Â±10-10 m

calculate the uncertainity in the position of an electron if the uncertainity in its velocity is 5.7*10 to the power 5 m/s(h=6.6*10 to the power -34js and m=9.1*10 to the power -31 kg)

calculate the uncertainity in the position of an electron if the uncertainity in its velocity is 5.710 to the power 5 m/s(h=6.610 to the power -34js and m=9.1*10 to the power -31 kg)