3. A star in a distant galaxy approaches the Sun at 3 X 106 m/s. It emits a photon with a wavelength of 0.4 microns. Apply the Doppler Effect to estimate the observed wavelength of this photon.
Radioactive decay
The emission of energy to produce ionizing radiation is known as radioactive decay. Alpha, beta particles, and gamma rays are examples of ionizing radiation that could be released. Radioactive decay happens in radionuclides, which are imbalanced atoms. This periodic table's elements come in a variety of shapes and sizes. Several of these kinds are stable like nitrogen-14, hydrogen-2, and potassium-40, whereas others are not like uranium-238. In nature, one of the most stable phases of an element is usually the most prevalent. Every element, meanwhile, has an unstable state. Unstable variants are radioactive and release ionizing radiation. Certain elements, including uranium, have no stable forms and are constantly radioactive. Radionuclides are elements that release ionizing radiation.
Artificial Radioactivity
The radioactivity can be simply referred to as particle emission from nuclei due to the nuclear instability. There are different types of radiation such as alpha, beta and gamma radiation. Along with these there are different types of decay as well.
![**Problem 3:**
A star in a distant galaxy approaches the Sun at a velocity of \(3 \times 10^6 \ \text{m/s}\). It emits a photon with a wavelength of 0.4 microns. Apply the Doppler Effect to estimate the observed wavelength of this photon.
**Explanation for Students:**
This problem involves using the Doppler Effect to determine how the motion of a star affects the wavelength of light observed from it. When a star moves towards us, the wavelengths of light we observe become shorter (a blueshift). The Doppler Effect equation for wavelength in the case of an approaching source is given by:
\[
\lambda' = \lambda \left( 1 - \frac{v}{c} \right)
\]
where:
- \(\lambda'\) is the observed wavelength,
- \(\lambda\) is the emitted wavelength,
- \(v\) is the velocity of the star relative to the observer,
- \(c\) is the speed of light (\(3 \times 10^8 \ \text{m/s}\)).
Use this formula to calculate the observed wavelength.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5009a5f7-cb0c-44c8-a915-95d249ae3d2b%2F580b9f60-1098-4c94-a813-aa0703a40711%2Fnmdh6ml_processed.png&w=3840&q=75)
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