Answer:
a) v = 1.567 10³ m / s , b) E = 4,278 10⁻¹⁹ J , c) E / K = 3.8 10⁵
Explanation:
a) For this exercise we will use the d’Broglie duality principle, which relates
p = h / λ
Where p is the moment, h the Planck constant that is worth .6.63 10⁻³⁴ J s and λ the wavelength
The momentum of a particle is defined by
p = mv
m v = h / λ
v = h / m λ
Reduce to SI units
λ = 465 nm (1m / 10⁹ nm) = 465 10⁻⁹ m
v = 6.63 10⁻³⁴ / (9.1 10⁻³¹ 465 10⁻⁹)
v = 1.567 10³ m / s
b) The Planck equation is
E = h f
The speed of light is
c = λ f
Let's replace
E = h c / λ
E = 6.63 10⁻³⁴ 3 10⁸/465 10⁻⁹
E = 4,278 10⁻¹⁹ J
c) The kinetic energy is
K = ½ m v²
K = ½ 9.1 10⁻³¹ (1.567 10³) 2
K = 11.17 10⁻²⁵ J
d) the energy ratio is
E / K = 4,278 10⁻¹⁹ / 1,117 10⁻²⁴
E / K = 3.8 10⁵
