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Question

The mass of an eletron is 9.1×1031 kg. If its kinetic energy is 3.0×1025 J. Calculate its de-broglie wavelength.

A
812 nm
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B
897 nm
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C
880 nm
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D
910 nm
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Solution

The correct option is B 897 nm
We know Kinetic energy (K.E) =12mv2
=12mv2=K.E.
v=(2K.Em)12
Putting the values according to the given data,
v=(2×3×1025 kg m2 s29.1×1031 kg)12
v=812 m s1
According to de-broglie wavelength
λ=hmv
=6.626×1034(9.1×1031 kg)(812 m s1)
=8967×1010 m=896.7 nm

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