What would be the speed of the following particles if they had the same wavelength as a photon of green light (λ = 500.0 nm)?
Proton (mass = 1.673*10^(-24)g) =_____
neutron (mass = 1.675*10(-24)g) =_____
electron (mass = 9.109*10^(-28)g) =_____
alpha particle (mass = 6.645*10^(-24)g) =____
To determine the speed of particles with the same wavelength as a photon of green light, we can use the de Broglie wavelength equation:
λ = h / p
where λ is the wavelength, h is the Planck's constant (6.626 x 10^(-34) J*s), and p is the momentum of the particle. The momentum of a particle is given by:
p = mv
where m is the mass of the particle and v is its velocity.
Let's calculate the speed for each particle:
1. Proton:
Given mass = 1.673 x 10^(-24) g
First, convert the mass to kg:
1.673 x 10^(-24) g = 1.673 x 10^(-27) kg
Now, we can find the speed:
λ = 500.0 nm = 500.0 x 10^(-9) m
Using the de Broglie equation, we find:
500.0 x 10^(-9) m = (6.626 x 10^(-34) J*s) / (1.673 x 10^(-27) kg * v)
Solving for v:
v = (6.626 x 10^(-34) J*s) / (1.673 x 10^(-27) kg * 500.0 x 10^(-9) m)
Calculating the speed of the proton will give you the answer.
2. Neutron:
Repeat the same steps as for the proton, but use the mass of the neutron (1.675 x 10^(-24) g) and solve for v to find the speed.
3. Electron:
Again, repeat the steps, but use the mass of the electron (9.109 x 10^(-28) g) and solve for v to find the speed.
4. Alpha particle:
Repeat the steps with the mass of the alpha particle (6.645 x 10^(-24) g) and solve for v to find the speed.
By following these instructions, you should be able to calculate the speed of each particle.