Question

What would be the speed of the following particles if they had the same wavelength as a photon of red light (λ = 750.0 nm)? If MASS or proton is 1.673x 10^-24?
nuetron is 1.675x 10^-24?
election is 9.109 x 10^-28?
alpha part 6.645x 10^-24 (grams)

Answer 1

$\lambda = \mathrm{h / mv}$, where

$\lambda$ is wavelength in m,

h is Planck's constant (6.626 x 10⁻³⁴ J*s),

m is mass in kg,

$m_p$ - the mass of proton

$m_n$ - the mass of neutron

$m_e$ - the mass of electron

ma.p - the mass of alpha part

v is speed in m/s.

To complete this problem you must convert your wavelength to meters and your mass to kilograms.

$$\lambda = 750.0 \mathrm{nm}(1 \mathrm{m}) / (1 \times 109 \mathrm{nm}) = 7.5 \times 10^{-7} \mathrm{m}$$ $$m_p = 1.673 \times 10^{-24} \mathrm{g}(1 \mathrm{kg}) / (1000 \mathrm{g}) = 1.673 \times 10^{-27} \mathrm{kg}$$

Rearrange the equation and solve for speed.

$$v = h / m \lambda = (6.626 \times 10^{-34} J * s) / (1.673 \times 10^{-27} kg) (7.5 \times 10^{-7} m) = 0.528 \mathrm{m/s}$$ $$m_n = 1.675 \times 10^{-24} \mathrm{g}(1 \mathrm{kg}) / (1000 \mathrm{g}) = 1.675 \times 10^{-27} \mathrm{kg}$$ $$v = h / m \lambda = (6.626 \times 10^{-34} J * s) / (1.675 \times 10^{-27} kg) (7.5 \times 10^{-7} m) = 0.527 \mathrm{m/s}$$ $$m_e = 9.109 \times 10^{-28} \mathrm{g}(1 \mathrm{kg}) / (1000 \mathrm{g}) = 9.109 \times 10^{-31} \mathrm{kg}$$ $$v = h / m \lambda = (6.626 \times 10^{-34} J * s) / (9.109 \times 10^{-31} kg) (7.5 \times 10^{-7} m) = 969.9 \mathrm{m/s}$$ $$m_{e,p} = 6.645 \times 10^{-24} \mathrm{g}(1 \mathrm{kg}) / (1000 \mathrm{g}) = 6.645 \times 10^{-27} \mathrm{kg}$$ $$v = h / m \lambda = (6.626 \times 10^{-34} J * s) / (6.645 \times 10^{-27} kg) (7.5 \times 10^{-7} m) = 0.133 \mathrm{m/s}$$