What is the wavelength, in meters, of an alpha particle with a kinetic energy of 8.010^-13 J. [mass of an alpha particle = 4.00150 amu; 1 amu = 1.6710^–27 kg]?

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Answer 1 · 2018-06-21T14:31:28

$6.4 × 10^-15\ "m"$

de-Broglie wavelength is given by

$λ = h/p$

Relation between $p$ and $"K"$ is

$p = sqrt("2Km")$

So, the wavelength now becomes

$λ = h/sqrt("2mK")$

Where

$λ = (6.626 × 10^-34\ "J s")/sqrt(2 × 4.00150 cancel"amu" × 1.67 × 10^-27\ "kg"/cancel"amu" × 8.0 × 10^-13\ "J")$

$color(white)(λ) = 6.4 × 10^-15\ "m"$

$color(white)(λ) = 6.4\ "fm"$

What is the wavelength, in meters, of an alpha particle with a kinetic energy of 8.0*10^-13 J. [mass of an alpha particle = 4.00150 amu; 1 amu = 1.67*10^–27 kg]?