The mass of an electron is 9.1 × 10^{-31}kg. If its K.E. is 3.0 × 10^{-25}J, calculate its wavelength.

ilovegarie3ay

ilovegarie3ay

Answered question

2022-12-24

The mass of an electron is 9.1 × 10 31 kg. If its K.E. is 3.0 × 10 25 J, calculate its wavelength.

Answer & Explanation

blasonavifdo

blasonavifdo

Beginner2022-12-25Added 10 answers

From de Broglie’s equation,
λ = h m v
Given, Kinetic energy (K.E) of the electron = 3.0 × 10 25 J
Since K . E = 1 2 m v 2
V e l o c i t y ( v ) = 2 K . E m
= 2 ( 3.0 × 10 25 J ) 9.10939 × 10 31 k g = 6.5866 × 10 4 v = 811.579 m s 1
Substituting the value in the expression of λ:
λ = 6.626 × 10 34 J s ( 9.10939 × 10 31 k g ) ( 811.579 m s 1 )
λ = 8.9625 × 10 7 m
Therefore, the wavelength of the electron is 8.9625 × 10 7 m.

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