Answer:
v = 2.2 * 10^(-24) m/s
Explanation:
Momentum is given in terms of wavelength as:
p = h/λ
Where h is Planck's constant = 6.626 * 10^(-34) kgm²/s
Hence, momentum will be:
p = 6.626 * 10^(-34) / (5.4 * 10^3 * 10^(-10)
p = 1.23 * 10^(-27) kgm/s
For a 56.7 g ball to have the same wavelength as green light, they must have the same momentum.
Momentum is given in terms of mass as:
p = m*v
p = 0.0567 * v
1.23 * 10^(-27) = 0.0567 * v
v = 1.23 * 10^(-27) / 0.0567
v = 2.2 * 10^(-24) m/s
Hence, it would have to move at a speed of 2.2 * 10^(-24) m/s to have the same wavelength.
Answer:
The tennis ball has a speed of [tex]2.16x10^{-26}m/s[/tex] in order to have that wavelength.
Explanation:
The wavelength of the electron can be determined by means of the de Broglie equation.
[tex]\lambda = \frac{h}{p}[/tex] (1)
Where h is the Planck's constant and p is the momentum
[tex]\lambda = \frac{h}{mv}[/tex] (2)
Therefore, v can be isolated from equation 2
[tex]v = \frac{h}{m\lambda}[/tex]
Notice that it is necessary to express the wavelength in units of meters and the mass in units of kilograms.
[tex]\lambda = 5.40x10^{3}Å .\frac{1x10^{-10}m}{1Å}[/tex] ⇒ [tex]5.4x10^{-7}m[/tex]
[tex]m = 56.7g .\frac{1Kg}{1000g}[/tex] ⇒ [tex]0.0567Kg[/tex]
[tex]v = \frac{6.624x10^{-34} J.s}{(0.0567Kg)(5.4x10^{-7}m)}[/tex]
But [tex]1J = Kg.m^{2}/s^{2}[/tex]
[tex]v = \frac{6.624x10^{-34} Kg.m^{2}/s^{2}.s}{(0.0567Kg)(5.4x10^{-7}m)}[/tex]
[tex]v = 2.16x10^{-26}m/s[/tex]
Hence, the tennis ball has a speed of [tex]2.16x10^{-26}m/s[/tex] in order to have that wavelength.
