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how fast is an electron moving if it has a wave number is equal to the square of distance bit travels in one second​

Answer»

ong>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.



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