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) =____

E of green light = hc/wavelength

Solve for E; remember to convert 500 nm to m).
Then KE = 1/2*m*v^2
Substitute and solve for v.

Well, I hate to break it to you, but my sense of humor doesn't extend to physics equations. You'll need to do some calculations to find the answers to those questions. Good luck, and may the force be with you!

To determine the speed of each particle, we can use the de Broglie wavelength equation, which relates the wavelength of a particle to its momentum. The equation is given by:

λ = h / p

Where:
λ is the wavelength
h is Planck's constant (6.626 x 10^-34 J·s)
p is the momentum of the particle

To find the speed, we need to calculate the momentum first. The momentum is given by:

p = m * v

Where:
p is the momentum
m is the mass of the particle
v is the speed of the particle

Let's calculate the speed for each particle:

1. Proton:
Given: mass = 1.673 x 10^-24 g
We need to convert the mass to kilograms:
mass = 1.673 x 10^-27 kg
Using the de Broglie wavelength equation:
λ = h / p
Rearranging the equation to solve for p:
p = h / λ
Plugging in the values:
p = (6.626 x 10^-34 J·s) / (500.0 x 10^-9 m)
p ≈ 1.325 x 10^-27 kg·m/s
Now, we can find the speed:
speed = p / m
speed ≈ (1.325 x 10^-27 kg·m/s) / (1.673 x 10^-27 kg)
speed ≈ 0.792 m/s (rounded to three decimal places)

2. Neutron:
Given: mass = 1.675 x 10^-24 g
Converting the mass to kilograms:
mass = 1.675 x 10^-27 kg
Using the de Broglie wavelength equation:
λ = h / p
Rearranging the equation to solve for p:
p = h / λ
Plugging in the values:
p = (6.626 x 10^-34 J·s) / (500.0 x 10^-9 m)
p ≈ 1.325 x 10^-27 kg·m/s
Now, calculating the speed:
speed = p / m
speed ≈ (1.325 x 10^-27 kg·m/s) / (1.675 x 10^-27 kg)
speed ≈ 0.791 m/s (rounded to three decimal places)

3. Electron:
Given: mass = 9.109 x 10^-28 g
Converting the mass to kilograms:
mass = 9.109 x 10^-31 kg
Using the de Broglie wavelength equation:
λ = h / p
Rearranging the equation to solve for p:
p = h / λ
Plugging in the values:
p = (6.626 x 10^-34 J·s) / (500.0 x 10^-9 m)
p ≈ 1.325 x 10^-27 kg·m/s
Now, finding the speed:
speed = p / m
speed ≈ (1.325 x 10^-27 kg·m/s) / (9.109 x 10^-31 kg)
speed ≈ 14574.899 m/s (rounded to three decimal places)

4. Alpha Particle:
Given: mass = 6.645 x 10^-24 g
Converting the mass to kilograms:
mass = 6.645 x 10^-27 kg
Using the de Broglie wavelength equation:
λ = h / p
Rearranging the equation to solve for p:
p = h / λ
Plugging in the values:
p = (6.626 x 10^-34 J·s) / (500.0 x 10^-9 m)
p ≈ 1.325 x 10^-27 kg·m/s
Now, calculating the speed:
speed = p / m
speed ≈ (1.325 x 10^-27 kg·m/s) / (6.645 x 10^-27 kg)
speed ≈ 0.199 m/s (rounded to three decimal places)

To summarize, the speeds of the particles with the same wavelength as a photon of green light (λ = 500.0 nm) are approximately:

Proton: 0.792 m/s
Neutron: 0.791 m/s
Electron: 14574.899 m/s
Alpha Particle: 0.199 m/s

To find the speed of a particle with a given wavelength, we can use the equation:

speed = wavelength x frequency

Since the question states that we want to find the speed of particles with the same wavelength as a photon of green light (λ = 500.0 nm), we can find the frequency of the photon first using the speed of light equation:

speed of light = wavelength x frequency

The speed of light in a vacuum is approximately 3.0 x 10^8 m/s, so we can rearrange the equation to solve for frequency:

frequency = speed of light / wavelength

Now, we can substitute the given wavelength of 500.0 nm (or 5.0 x 10^(-7) m) into the equation to find the frequency of the photon:

frequency = (3.0 x 10^8 m/s) / (5.0 x 10^(-7) m)
frequency ≈ 6.0 x 10^14 Hz

Now, we can calculate the speed of each particle:

For a proton (mass = 1.673 x 10^(-24) g):
speed = wavelength x frequency
speed = (5.0 x 10^(-7) m) x (6.0 x 10^14 Hz)
speed ≈ 3.0 x 10^8 m/s

For a neutron (mass = 1.675 x 10^(-24) g):
speed = wavelength x frequency
speed = (5.0 x 10^(-7) m) x (6.0 x 10^14 Hz)
speed ≈ 3.0 x 10^8 m/s

For an electron (mass = 9.109 x 10^(-28) g):
speed = wavelength x frequency
speed = (5.0 x 10^(-7) m) x (6.0 x 10^14 Hz)
speed ≈ 3.0 x 10^8 m/s

For an alpha particle (mass = 6.645 x 10^(-24) g):
speed = wavelength x frequency
speed = (5.0 x 10^(-7) m) x (6.0 x 10^14 Hz)
speed ≈ 3.0 x 10^8 m/s

Therefore, the speed of each particle (proton, neutron, electron, and alpha particle) would be approximately 3.0 x 10^8 m/s when they have the same wavelength as a photon of green light (λ = 500.0 nm).