Question

The wavelength LAMDA associated with a moving electron depends upon its

momentum p and Plank's constant h. Prove dimensionally that,
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Answer 1

Answer:lamda has the dimension of length

When we consider planks constant h

We know that E=hv

were E is energy, v is frequency

SI unit of E is Joule

were demetion of joule is =mass x (velocity)2

(E=mc2)

And frequency has demtion of 1/Time

then E=hv , h=E/v

So h has the dimension = mass x (velocity)2 xTime

And momentum p = mass x velocity

so h/p= mass x (velocity)2 x Time / mass x velocity

therefore h/p =Velocity x Time

(Velocity = length(distance)/ Time)

h/p= length/time x time = length

therefore dimension of lambda= h/p

so lambda is directly proportional to h/p

Explanation: