# LAST Question from the British Physics Olympiad

TLDRThis video provides a detailed walkthrough of a challenging physics problem related to star formation, utilizing the James Webb Space Telescope (JWST). The presenter explores various concepts including Wien's Law, ionization energy, photon calculation, and radiation pressure, among others. By solving complex equations, the video demonstrates how massive stars ionize surrounding regions, the energy they emit, and the subsequent impact on star formation in surrounding clouds. The problem concludes with calculations on photon travel time within the Sun and the role of neutrinos, offering insights into solar stability and physics Olympiad preparation tips.

###### Takeaways

- π The JWST telescope will reveal new physics about star formation, specifically how stars carve out ionized spheres.
- π‘ The temperature of the star (35,800 Kelvin) and the Sun's peak wavelength are used to calculate ionizing wavelengths using Wien's Law.
- π The calculated ionizing wavelength is 8.07 * 10^-8 meters, which leads to an energy high enough to ionize hydrogen (greater than 13.6 eV).
- β¨ The star emits a large number of ionizing photons per second, calculated to be approximately 2.30 * 10^49.
- π The radius of the ionizing bubble is approximately 2.76 light years, calculated using the number of ionizing photons.
- β One large star with a radius of 2.76 light years can photoevaporate a pillar in a nebula, potentially triggering further star formation.
- π‘ Radiation pressure from the star contributes to the collapse of nearby cloud mass, forming a new star cluster.
- π Gravitational pressure within the star is nearly 1 million times stronger than the outward radiation pressure.
- π It takes approximately 44,000 years for a photon to travel from the Sun's center to its surface, due to continuous absorption and re-emission.
- π Neutrinos provide insights into the Sun's energy output, with minimal fluctuations in energy production over 44,000 years, indicating the Sun's stability.

###### Q & A

### What is the James Webb Space Telescope (JWST) expected to reveal about star formation?

-The JWST is expected to uncover fascinating physics about star formation, including the process by which a newly born star carves out a sphere in the surrounding nebula.

### What is the significance of Wien's Law in the context of the JWST's observations?

-Wien's Law states that the product of a star's surface temperature and its peak wavelength is a constant. This principle is used to calculate the peak wavelength of light emitted by a star, which can then be used to determine if the emitted light is ionizing.

### What is the temperature of the star mentioned in the script, and how does it relate to the ionization of hydrogen?

-The star's temperature is given as 35,800 Kelvin. This temperature is used to calculate the ionizing wavelength and energy of the star's emitted light, which is found to be sufficient for ionizing hydrogen, as it is higher than the ionization energy of 13.6 electron volts.

### How is the ionizing energy of the star's emitted light calculated in electron volts?

-The ionizing energy is calculated by first determining the wavelength of the emitted light using Wien's Law, then converting the energy from joules to electron volts by dividing by the elementary charge.

### What is the role of the ionizing photons in shaping the nebula around a star?

-The ionizing photons emitted by a star can carve out a sphere in the surrounding nebula, creating an ionized region. The number of these photons can be calculated using the star's luminosity and the energy of each photon.

### How is the radius of the ionized bubble around a star calculated?

-The radius of the ionized bubble is calculated using the number of ionizing photons emitted by the star per second, along with the density of hydrogen in the nebula and other physical constants.

### What is the significance of the number of large stars needed to photoevaporate a pillar in the script?

-The number of large stars required to photoevaporate a pillar indicates the intensity of the radiation pressure needed to disperse the gas and dust in the pillar, making it no longer visible.

### How is the mass of a cloud that will collapse to form a new star cluster calculated in Part B of the script?

-The mass of the collapsing cloud is calculated using an equation that relates the cloud's temperature, pressure, and the mass of hydrogen, along with physical constants like Boltzmann's constant and the gravitational constant.

### What is the importance of understanding the pressures within a star as described in the script?

-Understanding the pressures within a star is crucial for studying stellar structure and evolution. The balance between gravitational pressure, which tries to collapse the star, and radiation and gas pressure, which opposes this collapse, is essential for the star's stability.

### How long does it take for a photon to travel from the center of the Sun to its surface, and why does it take this long?

-It takes approximately 44,000 years for a photon to travel from the center of the Sun to its surface due to the continuous process of absorption and reemission as it moves through the solar medium.

### What insights can be gained from studying neutrinos emitted by the Sun?

-Neutrinos, which hardly interact with matter, provide valuable information about the Sun's core. By studying the flux and energy of these neutrinos, scientists can learn about the Sun's energy production processes and its stability over time.

###### Outlines

##### π JWST and Star Formation Physics

##### π‘ Calculating Ionizing Photon Numbers

##### π Triggering Star Formation

##### βοΈ Balancing Pressures in Star Formation

##### π The Long Journey of Photons

##### π Neutrinos and Solar Stability

###### Mindmap

###### Keywords

##### π‘Wien's Law

##### π‘Ionizing Radiation

##### π‘Luminosity

##### π‘Photon

##### π‘Nebula

##### π‘Pressure

##### π‘Gravitational Pressure

##### π‘Mean Free Path

##### π‘Neutrinos

##### π‘Solar Mass

###### Highlights

The plan for solving the problem involves using Wien's Law to determine the wavelength corresponding to the surface temperature of the star.

Calculation of the ionizing energy confirms that the energy is sufficient to ionize hydrogen, leading to the formation of an ionized region.

The problem introduces the concept of monochromatic emission from the star, which simplifies the calculation of the number of ionizing photons per second.

Using the given luminosity, the total number of ionizing photons is calculated, showing how a star can carve out an ionizing bubble in a nebula.

The calculation of the radius of the ionizing bubble is completed, yielding a value in light years.

The number of large stars required to photo-evaporate the pillar is determined to be just one, indicating the significant impact of massive stars.

The radiation pressure from the star is calculated and used to determine the mass that will collapse under this pressure to form a new star cluster.

The problem examines the balance between gravitational pressure and outward radiation pressure within the star, calculating the mass and pressure at the center.

A comparison is made between the radiation pressure and gravitational pressure, showing that gravitational pressure is nearly a million times stronger.

The problem explores the journey of photons from the center of the Sun to its surface, highlighting the significant time delay due to continuous absorption and re-emission.

The concept of the mean free path is introduced to calculate the distance a photon travels between absorptions, yielding a distance of about 1.16 mm.

The final part of the problem involves calculating the number of neutrinos detected on Earth, which correspond to 92% of the Sun's energy output.

The stability of the Sun's energy production over the last 44,000 years is discussed, with a small percentage difference indicating minimal fluctuations.

The problem emphasizes the significance of studying neutrinos to understand the long-term stability and energy production of the Sun.

The problem-solving process demonstrates a thorough understanding of astrophysical concepts, including Wien's Law, radiation pressure, and the behavior of neutrinos.

###### Transcripts

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