Question

What would the speed of each particle be if it had the same wavelength as a photon of violet light ( λ = 400.0 nm ) ?

a. proton ( mass = 1.673 × 10 − 24 g ) speed: m / s
b. neutron ( mass = 1.675 × 10 − 24 g ) speed: m / s
c. electron ( mass = 9.109 × 10 − 28 g ) speed: m / s
d. alpha particle ( mass = 6.645 × 10 − 24 g ) speed:

Answer 1

To develop this problem we will use the DeBroglie relationship for which the wavelength is considered as

$\lambda = \frac{h}{mv}$

Where,

h = Planck's constant

m = mass

v = Velocity

$\lambda$ = Wavelength

Rearranging the equation we have that the speed would be

$v = \frac{h}{m\lambda}$

Our given values are considered

$\lambda = 400nm = 4*10^{-7}m$

$h = 6.626*10^{-34} J\cdot s$

$m = 1.673*10^{-24}g = 1.673*10^{-27}kg$

The value of the mass varies, therefore its speed would be given as:

Proton $(m=1.673*10^{-27}kg)$

$v = \frac{6.626*10^{-34}}{(1.673*10^{-27})(4*10^{-7})}$

$v = 0.99m/s$

Neutron  $(m=1.675*10^{-27}kg)$

$v = \frac{6.626*10^{-34}}{(1.675*10^{-27})(4*10^{-7})}$

$v = 0.988m/s$

Electron $(m=9.109*10^{-31}kg)$

$v = \frac{6.626*10^{-34}}{(9.109*10^{-31})(4*10^{-7})}$

$v = 1818.53m/s$

Alpha particle $(m=6.645*10^{-27} kg)$

$v = \frac{6.626*10^{-34}}{(6.645*10^{-27} )(4*10^{-7})}$

$v = 0.249m/s$