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Calculate the de Broglie wavelength of an electron accelerated from rest through a potential difference of (a) 100 V, (b) 1.0 kV, (c) 100 kV.

User Dullson
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1 Answer

7 votes

Answer:

(a)
\lambda=1.227\ A

(b)
\lambda=0.388\ A

(c)
\lambda=0.038\ A

Step-by-step explanation:

Given that,

(a) An electron accelerated from rest through a potential difference of 100 V. The De Broglie wavelength in terms of potential difference is given by :


\lambda=(h)/(√(2meV) )

Where

m and e are the mass of and charge on an electron

On solving,


\lambda=(12.27)/(√(V) )\ A

V = 100 V


\lambda=(12.27)/(√(100) )\ A


\lambda=1.227\ A

(b) V = 1 kV = 1000 V


\lambda=(12.27)/(√(V) )\ A


\lambda=(12.27)/(√(1000) )\ A


\lambda=0.388\ A

(c) If
V=100\ kV=10^5\ V


\lambda=(12.27)/(√(10^5) )\ A


\lambda=0.038\ A

Hence, this is the required solution.

User Iwis
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