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

Answer 1

Use the DeBroglie wavelength formula

Wavelength = h / (mass x velocity)

Velocity = h / (mass x wavelength)

h = 6.626 x 10^-34 J∙s

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 J∙s) / { (9.10939 x 10^-31 Kg) (575 x 10^-9 m) }

             = (6.626 x 10^-34 m² Kg s^-2∙s) / (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 J∙s) / { (1.67262 x 10^-27 Kg) (575 x 10^-9 m) }

             = (6.626 x 10^-34 m² Kg s^-2∙s) / (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 J∙s) / { (1.67493 x 10^-27 Kg) (575 x 10^-9 m) }

             = (6.626 x 10^-34 m² Kg s^-2∙s) / (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 J∙s) / { (6.64 x 10^-27 Kg) (575 x 10^-9 m) }

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

             = 1.735 x 10^-1 m s^-1