Question

How fast is an electron moving if it has a wavelength equal to the distance it travels in one second?

Answer 1

Answer:

Now, this is an interesting question!! Let’s understand this question by solving it mathematically.

Explanation:

The De Broglie’s relation gives us the relation between a moving particle’s wavelength with its momentum in other words it tells us that a particle can exhibit the properties of waves, i.e.

λ = h/p= h/mv

where λ= wavelength

          h= Plank’s Constant

          p = momentum

         m= mass of a particle

          v= velocity of the mass

Here we are given that wavelength is equal to the distance travelled by the electron in 1 second, i.e.

λ = h/(m * (1 second))

Now let’s solve for v:

v^2= h/(m * (1 second))

v = √((h)/(m*(1 Second)))

where Plank’s Constant, h = 6.626 x 10¯34 J s

mass of electron, m = 9.10939 x 10¯31 kg

Place the values for h and m in the above equation that we have solved for v, i.e.  

v = √((6.626 x 10¯34 J s)/(9.10939 x 10¯31 kg*(1 Second)))

v = 0.027 m/s

Therefore, the electron is moving with a velocity of 0.027 m/s.

Hope this solution is helpful and clears all your doubt.