Question

An electron has a speed of 40m/s accurate upto 99.99%. what is the uncertainty in locating its position

Answer 1

Mass of electron = 9.1 X 10-31 kg.

uncertainty in position = Planck’s constant / 4 * pi * mass * uncertainty in velocity.

Planck's constant is given the symbol h in physics and numerically is equal to 6.63 x 10^-34 Joule seconds.

So, uncertainty =6.63x10^-34/4x3.14x9.1x10^-31x 40x0.9999

=6.63x10^-65/4x3.14x9.1x39.996

=0.001450327x10^-6

5=1.45x10^-68

Answer 2

Answer:

According to uncertainty principle,

Δx . mΔv = h/4π or Δx = h/4π mΔv

Δv = 40 m/s (accurate up to 99.99%)

= (100-99.99)/100 * 40 m/s

= (0.01/100)*40

= 4 x 10^-3 m/s

m = 9.1 x 10^-31 kg

h = 6.626 x10^-34 kgm^2/s, π =3.14

∆x = h4πm.∆v∆x = 6.626×10−344×3.14×9.1×10−31 ×4×10−3∆x = 0.0144 m