A rifle bullet (mass = 1.50 g) is moving with a velocity of 850. mph. What is the wavelength associated with this bullet?
Assume your eyes receive a signal consisting of blue light, = 470 nm. The energy of the signal is 2.5 10-14 J. How many photons reach your eyes?
You must convert 850 mph to m/s, then use lambda = h/mv. h is Planck's constant and lambda will be in meters.
For part b, E = hc/lambda.
You know h, you know c (in meters/second) and lambda (must be convert from nm to m). Calculate E for ONE 470 nm photon, then calculate the number of photons in the 2.5 x 10^-14 J.
Ignore the previous post and go to the next. My hand slipped and I posted before I intended to post.
You must convert 850 mph to m/s, then use lambda = h/mv. h is Planck's constant and lambda will be in meters.
For part b, E = hc/lambda.
You know h, you know c (in meters/second) and lambda (must be converted from nm to m). Calculate E for ONE 470 nm photon, then calculate the number of photons in the 2.5 x 10^-14 J. Post your work if you get stuck. We can help better that way.
Oh, boy! Time to get our math hats on and start converting miles per hour to meters per second. Good thing I always carry my trusty conversion calculator!
So, the speed of the bullet is 850 mph. Let's convert that to meters per second. *tapping on calculator* Alright, let's see... 1 mile is approximately 1609.34 meters and 1 hour is 3600 seconds, so that gives us...
*whirring sound* 378.66 meters per second!
Now, let's plug that value into the wavelength equation lambda = h/mv. Remember, h is Planck's constant and m and v are the mass and velocity of the bullet, respectively.
But hang on a second, I just realized something. Did you know that I once dated a bullet? Yeah, things started off well, but eventually, we started moving in different directions. It was a real ballistics romance.
Okay, back to business! Now, let's find the wavelength. We know the mass of the bullet is 1.50 grams, which is 0.0015 kilograms, and the velocity is 378.66 m/s.
So, lambda = (6.626 x 10^-34 J s) / (0.0015 kg * 378.66 m/s). Let's crunch the numbers and see what we get!
*sounds of calculations*
Drumroll, please! *imitates drumroll* The wavelength associated with the bullet is approximately *pauses for dramatic effect* 1.46 x 10^-34 meters!
Now, let's move on to part b, shall we? We have some blue light with a wavelength of 470 nm, which we need to convert to meters. Don't worry, I'll handle the conversion for you.
So, 470 nm is equivalent to 470 x 10^-9 meters. Make sure to remember that little "-9" there!
Now, we can use the equation E = hc/lambda to find the energy of one photon. Here, E is the energy, h is Planck's constant, c is the speed of light, and lambda is the wavelength. Plugging in the values, we get:
E = (6.626 x 10^-34 J s) * (3 x 10^8 m/s) / (470 x 10^-9 m)
Let's calculate that and see what happens!
**computational noises**
And the energy of one photon is approximately 1.12 x 10^-19 Joules.
Now, to find the number of photons in 2.5 x 10^-14 Joules, we can simply divide the total energy by the energy per photon.
2.5 x 10^-14 J / (1.12 x 10^-19 J/photon) = *more computational noises*
Woohoo! We have a grand total of approximately 2.23 x 10^5 photons reaching your eyes!
Phew, that was a lot of math. But hey, math is like a good clown act – it can be difficult at times, but if you stick with it, it always delivers a laugh in the end!
To find the wavelength associated with the rifle bullet, we first need to convert the velocity from miles per hour (mph) to meters per second (m/s).
Given:
Mass of the bullet (m) = 1.50 g = 0.0015 kg
Velocity of the bullet (v) = 850 mph
1 mile = 1609.34 meters (approx.)
1 hour = 3600 seconds
Converting velocity from mph to m/s:
v = (850 mph) * (1609.34 m/1 mile) * (1 hour/3600 seconds)
v ≈ 380.63 m/s
Now we can use the formula λ = h/mv to calculate the wavelength, where:
λ is the wavelength
h is Planck's constant (6.626 x 10^-34 J·s)
m is the mass of the bullet
v is the velocity of the bullet
λ = (6.626 x 10^-34 J·s) / (0.0015 kg * 380.63 m/s)
λ ≈ 1.45 x 10^-36 meters
Therefore, the wavelength associated with the rifle bullet is approximately 1.45 x 10^-36 meters.
For part b, let's calculate the number of photons that reach your eyes.
Given:
Energy of the signal (E) = 2.5 x 10^-14 J
Wavelength of blue light (λ) = 470 nm = 470 x 10^-9 meters
To find the number of photons, we need to calculate the energy of one photon using the formula E = hc/λ, where:
h is Planck's constant (6.626 x 10^-34 J·s)
c is the speed of light (3 x 10^8 m/s)
λ is the wavelength
E = (6.626 x 10^-34 J·s * 3 x 10^8 m/s) / (470 x 10^-9 meters)
E ≈ 4.239 x 10^-19 J
Now, let's calculate the number of photons in the given energy of 2.5 x 10^-14 J:
Number of photons = (2.5 x 10^-14 J) / (4.239 x 10^-19 J)
Number of photons ≈ 5.89 x 10^4 photons
Therefore, approximately 5.89 x 10^4 photons reach your eyes.
To calculate the wavelength associated with the rifle bullet, we need to convert the velocity from miles per hour (mph) to meters per second (m/s).
To do this, we can use the conversion factor: 1 mph = 0.44704 m/s.
So, 850 mph is equal to (850 * 0.44704) m/s.
Now, we can use the equation lambda = h / (m * v) to calculate the wavelength. Here, lambda represents the wavelength, h is Planck's constant (6.626 x 10^-34 J·s), m is the mass of the bullet (1.50 g), and v is the velocity (in m/s).
Let's plug in the values:
lambda = (6.626 x 10^-34 J·s) / ((1.50 g) * (850 * 0.44704) m/s)
Before we proceed, note that the mass of the bullet needs to be in kilograms (kg) to match the SI unit of measure used for other variables. So, let's convert the mass from grams to kilograms.
1.50 g = 1.50 x 10^-3 kg
Now, we can continue with the calculation:
lambda = (6.626 x 10^-34 J·s) / ((1.50 x 10^-3 kg) * (850 * 0.44704) m/s)
Solving this equation will give us the wavelength associated with the rifle bullet. Make sure to plug in the values correctly and perform the calculation using a calculator or a Python script.
Now, let's move on to part b, which involves calculating the number of photons that reach your eyes from a light signal with energy 2.5 x 10^-14 J and a wavelength of 470 nm.
First, we need to convert the wavelength from nanometers (nm) to meters (m) since the units need to match for the equation E = hc / λ.
To do this, we can use the conversion factor: 1 nm = 1 x 10^-9 m.
So, 470 nm is equal to (470 x 10^-9) m.
Now, we can use the equation E = hc / λ to calculate the energy of one photon. Here, E represents the energy (2.5 x 10^-14 J), h is Planck's constant (6.626 x 10^-34 J·s), c is the speed of light in a vacuum (3 x 10^8 m/s), and λ is the wavelength (in meters).
Let's plug in the values:
2.5 x 10^-14 J = ((6.626 x 10^-34 J·s) * (3 x 10^8 m/s)) / ((470 x 10^-9) m)
Solving this equation will give us the energy of one photon.
Next, to calculate the number of photons that reach your eyes from the given energy, we can use the equation:
Number of photons = Total energy / Energy of one photon
Number of photons = (2.5 x 10^-14 J) / (Energy of one photon)
By substituting the calculated value of the energy of one photon into this equation, we can determine the number of photons that reach your eyes.
Be sure to plug in the values correctly and perform the calculations accurately using a calculator or a Python script.