How rapidly would the following particles be moving if they all had the same wav

Question

How rapidly would the following particles be moving if they all had the same wavelength as a photon of yellow light (lamda=575.0) answer in m/s -an electron of a mass 9.10939*10^-28g -a proton of a mass 1.67262*10^-24g -a proton of a mass 1.67493*10^-24g -an alpha particle mass 6.64*10^-24g How rapidly would the following particles be moving if they all had the same wavelength as a photon of yellow light (lamda=575.0) answer in m/s -an electron of a mass 9.10939*10^-28g -a proton of a mass 1.67262*10^-24g -a proton of a mass 1.67493*10^-24g -an alpha particle mass 6.64*10^-24g -an electron of a mass 9.10939*10^-28g -a proton of a mass 1.67262*10^-24g -a proton of a mass 1.67493*10^-24g -an alpha particle mass 6.64*10^-24g

Explanation / Answer

Use the DeBroglie wavelength formula

Wavelength = h / (mass x velocity)

Velocity = h / (mass x wavelength)

h = 6.626 x 10-34 Js

lamda=575 nm = 575 x 10-9 m

(a) Electron

Mass = 9.10939 x 10-28 g = 9.10939 x 10-31 Kg

Velocity = h / (mass x wavelength)

             = (6.626 x 10-34 Js) / { (9.10939 x 10-31 Kg) (575 x 10-9 m) }

             = (6.626 x 10-34 m2 Kg s-2s) / (5237.899 x 10-40 Kg m) [ J = m2 Kg s-2 ]

             = 1.265 x 103 m s-1

(b) Proton

Mass = 1.67262 x 10-24 g = 1.67262 x 10-27 Kg

Velocity = h / (mass x wavelength)

             = (6.626 x 10-34 Js) / { (1.67262 x 10-27 Kg) (575 x 10-9 m) }

             = (6.626 x 10-34 m2 Kg s-2s) / (961.76 x 10-36 Kg m) [ J = m2 Kg s-2 ]

             = 6.89 x 10-1 m s-1

(c) Proton

Mass = 1.67493 x 10-24 g = 1.67493 x 10-27 Kg

Velocity = h / (mass x wavelength)

             = (6.626 x 10-34 Js) / { (1.67493 x 10-27 Kg) (575 x 10-9 m) }

             = (6.626 x 10-34 m2 Kg s-2s) / (963.08 x 10-36 Kg m) [ J = m2 Kg s-2 ]

             = 6.88 x 10-1 m s-1

(d) Alpha particle

Mass = 6.64 x 10-24 g = 6.64 x 10-27 Kg

Velocity = h / (mass x wavelength)

             = (6.626 x 10-34 Js) / { (6.64 x 10-27 Kg) (575 x 10-9 m) }

             = (6.626 x 10-34 m2 Kg s-2s) / (3.818 x 10-33 Kg m) [ J = m2 Kg s-2 ]

             = 1.735 x 10-1 m s-1

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