For a I got 36666.67 seconds which I don't know if its right and then b I know my answer is wrong because I got 0.0375 for wavelength.And I don't understand how to do e or f.
The Voyager 1 spacecraft is at the edge of the solar system, about 11 billion km away. (a) How
long does a radio signal from Voyager 1 take to get to the Earth? (b) Its radio works at 8 GHz.
What is the wavelength? (c) What type of light is this? (d) What is the energy of 1 photon? (e)
It has a 23 watt radio wave transmitter. How many photons per second is this? (f) This radio
wave is aimed towards the Earth by a dish; by the time the signal gets to the Earth, the area of
the radio beam is 4x10^15 km^2
. What is the photon flux density, in photons per second per square
km? (g) How about in photons per second per square meter?
a. t = d/V = 11*10^12m/(3*10^9m/s) = 3667 s. = 1.02 h.
b. Wavelength = V/f = 3*10^8m/s/(8*10^9c/s) = 0.0375 m.
To solve these problems, we'll need to use some basic physics formulas and conversions. Here's a step-by-step guide on how to approach each part of the question:
(a) To find how long a radio signal from Voyager 1 takes to reach Earth, we'll divide the distance by the speed of light.
1. Convert the distance from kilometers to meters: 11 billion km = 11 × 10^12 m.
2. Divide the distance by the speed of light: 11 × 10^12 m / (3 × 10^8 m/s) = 36,666.67 seconds.
So, the signal takes approximately 36,666.67 seconds to reach Earth.
(b) To find the wavelength, we'll use the formula λ = c/f, where λ represents wavelength, c represents the speed of light, and f represents frequency.
1. Convert the frequency from gigahertz to hertz: 8 GHz = 8 × 10^9 Hz.
2. Substitute the values into the formula: λ = (3 × 10^8 m/s) / (8 × 10^9 Hz) = 0.0375 meters.
(c) To determine the type of light, we'll need to compare the wavelength with the electromagnetic spectrum. Here are some common types of light and their corresponding wavelengths:
- Radio waves: Wavelengths greater than 1 meter.
- Microwaves: Wavelengths from 1 mm to 1 meter.
- Infrared: Wavelengths from 700 nm to 1 mm.
- Visible light: Wavelengths from 400 nm to 700 nm.
- Ultraviolet: Wavelengths from 10 nm to 400 nm.
- X-rays: Wavelengths from 10 pm to 10 nm.
- Gamma rays: Wavelengths less than 10 pm.
Since the wavelength of the radio signal is 0.0375 meters, it falls within the radio wave range.
(d) To calculate the energy of one photon, we'll use the equation E = hf, where E represents energy, h represents Planck's constant (6.63 × 10^-34 J·s), and f represents frequency.
1. Substitute the frequency into the equation: E = (6.63 × 10^-34 J·s) × (8 × 10^9 Hz) = 5.304 × 10^-24 J.
So, the energy of one photon is 5.304 × 10^-24 Joules.
(e) To find the number of photons per second from a 23-watt radio wave transmitter, we'll divide the power by the energy of one photon.
1. Convert the power from watts to joules/second: 23 watts = 23 joules/second.
2. Divide the power by the energy of one photon: 23 joules/second / (5.304 × 10^-24 J) = approximately 4.33 × 10^24 photons/second.
Therefore, the radio wave transmitter emits approximately 4.33 × 10^24 photons per second.
(f) To determine the photon flux density, we'll divide the number of photons per second by the area of the radio beam.
1. Convert the area from square kilometers to square meters: 4 × 10^15 km^2 = 4 × 10^21 m^2.
2. Divide the number of photons per second by the area: (4.33 × 10^24 photons/second) / (4 × 10^21 m^2) = approximately 1.08 × 10^3 photons/second/m^2.
So, the photon flux density is approximately 1.08 × 10^3 photons per second per square meter.
(g) To determine the photon flux density per square kilometer, we'll multiply the photon flux density per square meter by the conversion factor for square meters to square kilometers.
1. Multiply the photon flux density per square meter by the conversion factor: (1.08 × 10^3 photons/second/m^2) × (10^-6 km^2/m^2) = approximately 1.08 photons/second/km^2.
Therefore, the photon flux density is approximately 1.08 photons per second per square kilometer.
I hope this step-by-step guide helps you understand how to approach each part of the question!