1. Calculate the frequency (Hz) and energy (eV) of green photons with wavelength of 555nm. Photon energy = hν, where ν = frequency in Hz and h = 6.626x10-34 joule-sec, the Planck’s constant. Keep in mind that: wavelengthxfrequency = speed.
2. Andy Ru can serve tennis balls at 140 mile per hour. When the ball is frying at this speed, calculate the kinetic energy and express it in Joules. You would need to measure the mass of a tennis ball in grams. For your information, 1 oz. = 454 grams/16 = 28.4 grams.
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1. To calculate the frequency of green photons with a wavelength of 555nm, we can use the equation:
speed = wavelength x frequency
The speed of light is approximately 3.00 x 10^8 m/s.
First, we need to convert the wavelength from nanometers to meters:
Wavelength = 555nm = 555 x 10^-9 m
Now we can rearrange the equation to solve for the frequency:
frequency = speed / wavelength
frequency = (3.00 x 10^8 m/s) / (555 x 10^-9 m)
frequency ≈ 5.41 x 10^14 Hz
Now, to calculate the energy of a photon, we can use the equation:
energy (eV) = h x frequency
where h = 6.626 x 10^-34 J·s (Planck's constant)
First, let's convert Planck's constant h to electron volts (eV):
1 eV = 1.6 x 10^-19 J
So, h (eV·s) = h (J·s) / (1.6 x 10^-19 J)
h (eV·s) ≈ (6.626 x 10^-34 J·s) / (1.6 x 10^-19 J)
h (eV·s) ≈ 4.14 x 10^-15 eV·s (approx.)
Now, we can calculate the energy:
energy (eV) = h (eV·s) x frequency (Hz)
energy (eV) ≈ (4.14 x 10^-15 eV·s) x (5.41 x 10^14 Hz)
energy (eV) ≈ 2.24 eV (approx.)
Therefore, the frequency of the green photons is approximately 5.41 x 10^14 Hz and the energy of each photon is approximately 2.24 eV.
2. To calculate the kinetic energy of the tennis ball, we can use the equation:
kinetic energy = 0.5 x mass x velocity^2
First, we need to convert the speed from miles per hour to meters per second:
Speed = 140 miles/hour
1 mile ≈ 1609 meters
Speed = (140 miles/hour) x (1609 meters/1 mile) x (1 hour/3600 seconds)
Speed ≈ 62.5 m/s (approx.)
Next, we need to find the mass of the tennis ball. Let's assume it is 57 grams (approximately 2 ounces).
Now we can calculate the kinetic energy:
Kinetic energy = 0.5 x mass x velocity^2
Kinetic energy = 0.5 x (57 grams) x (62.5 m/s)^2
Kinetic energy ≈ 112,031.25 Joules (approx.)
Therefore, the kinetic energy of the tennis ball when served at 140 miles per hour is approximately 112,031.25 Joules.
To calculate the frequency (Hz) and energy (eV) of green photons with a wavelength of 555 nm, you can use the following steps:
1. Convert the wavelength from nanometers (nm) to meters (m):
555 nm = 555 x 10^-9 m
2. Use the wave equation: wavelength x frequency = speed.
Rearrange the equation to solve for frequency:
frequency = speed / wavelength
3. The speed of light (c) is approximately 299,792,458 meters per second (m/s).
4. Calculate the frequency:
frequency = (299,792,458 m/s) / (555 x 10^-9 m)
Simplifying the calculation, frequency = 5.40 x 10^14 Hz
5. Now, to calculate the energy of the photon, use the formula: photon energy = hν.
Given that Planck's constant (h) is 6.626 x 10^-34 joule-sec, and frequency (ν) is 5.40 x 10^14 Hz, we can substitute these values into the formula:
photon energy = (6.626 x 10^-34 joule-sec) x (5.40 x 10^14 Hz)
= 3.57 x 10^-19 Joules
Therefore, the frequency of the green photons with a wavelength of 555 nm is approximately 5.40 x 10^14 Hz, and the energy of each photon is approximately 3.57 x 10^-19 Joules.
Moving on to the second question:
To calculate the kinetic energy of a tennis ball traveling at 140 miles per hour, we need to follow these steps:
1. Convert the speed from miles per hour (mph) to meters per second (m/s):
140 mph = (140 x 1609.34 m) / (1 h x 3600 s) ≈ 62.35 m/s
2. Measure the mass of the tennis ball in grams (g):
1 oz = 28.4g
3. Convert grams to kilograms (kg):
28.4 g = 0.0284 kg
4. Use the formula for kinetic energy: kinetic energy = (1/2) x mass x velocity^2
kinetic energy = (1/2) x (0.0284 kg) x (62.35 m/s)^2
≈ 55.7 Joules
Therefore, the kinetic energy of the tennis ball traveling at 140 miles per hour is approximately 55.7 Joules.