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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 |
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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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