Determine the de-Broglie wavelength of a proton whose kinetic is equal to rest mass energy of an electron (rest mass energy = m0c2 & mp = 1840me )

given :

kinetic energy = rest mass energy

or

K = m0c2

so, deBroglie wavelength will be

λ = h / (2m0K)1/2

or

= h / (2m0.m0c2)1/2

so,

λ = h / (2m02c2)1/2 = h / (m0c√2)

here 

h = 6.63 x 10-34 J.s

m0 = 1840me = 1840 x 9.1 x 10-31 kg = 1.67 x 10-27 kg

c = 3.8 x 108 m/s

thus,

λ = 6.63 x 10-34 / [ 1.67 x 10-27 x 3.8 x 108 x √2] 

so, the wavelength of the proton will be

λ = 0.738 x 10-15 m

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