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Consider a kilogram of stellar material comprising 50% H and 50% He by number of atoms. (a) What are the mass fractions of H and He in this gas? (b) What is the mean atomic weight of the gas when neutral? And when fully ionized? (Note: the me weight can be taken as the mean mass per free particle in atomic mass units.) (c) Assuming that the gas is neutral, find the number of H atoms in this gas. Hence find the energy re fully ionize all the H, in both electron volts and joules. How does this compare with average New household energy consumption? (d) Also find the amount of onorar (in oW ond I) required to fully ionizo all the Ho (to giro Ho L

Consider a kilogram of stellar material comprising 50% H and 50% He by number of atoms. (a) What are the mass fractions of H and He in this gas? (b) What is the mean atomic weight of the gas when neutral? And when fully ionized? (Note: the me weight can be taken as the mean mass per free particle in atomic mass units.) (c) Assuming that the gas is neutral, find the number of H atoms in this gas. Hence find the energy re fully ionize all the H, in both electron volts and joules. How does this compare with average New household energy consumption? (d) Also find the amount of onorar (in oW ond I) required to fully ionizo all the Ho (to giro Ho L

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Useful data: G = 6.7 × 10-¹¹ Nm²kg-2, 1.0eV = 2.0 × 10³⁰kg, R₁ = 7 × 10³m, 13.6eV, Eion,He0 = 24.5eV, Mo Eion, H k = 1.38 × 10-23 JK-1, Avogadro's number NA Consider a kilogram of stellar material comprising 50% H and 50% He by number of atoms. - = 1.60 × 10-19 J Lo - 3.9 × 1026 W Eion,He+ = 54.4eV = 6.0 × 1023 mole -1 (a) What are the mass fractions of H and He in this gas? (b) What is the mean atomic weight of the gas when neutral? And when fully ionized? (Note: the mean atomic weight can be taken as the mean mass per free particle in atomic mass units.) (c) Assuming that the gas is neutral, find the number of H atoms in this gas. Hence find the energy required to fully ionize all the H, in both electron volts and joules. How does this compare with average New Zealand household energy consumption? (d) Also find the amount of energy (in eV and J) required to fully ionize all the He (to give He++). Hence find the total energy required to ionize all the gas (in J). 3 (e) Compare the energy required for full ionization (from (d), in joules) with the thermal energy (in joules) in the gas at 106 K, given that each particle has thermal energy / kT. (Don't forget to include the thermal energy of all the free electrons as well as the positive ions.) From your answer, is it probable that this gas mixture is fully ionized at a temperature of one million kelvin?
Transcribed Image Text:Useful data: G = 6.7 × 10-¹¹ Nm²kg-2, 1.0eV = 2.0 × 10³⁰kg, R₁ = 7 × 10³m, 13.6eV, Eion,He0 = 24.5eV, Mo Eion, H k = 1.38 × 10-23 JK-1, Avogadro's number NA Consider a kilogram of stellar material comprising 50% H and 50% He by number of atoms. - = 1.60 × 10-19 J Lo - 3.9 × 1026 W Eion,He+ = 54.4eV = 6.0 × 1023 mole -1 (a) What are the mass fractions of H and He in this gas? (b) What is the mean atomic weight of the gas when neutral? And when fully ionized? (Note: the mean atomic weight can be taken as the mean mass per free particle in atomic mass units.) (c) Assuming that the gas is neutral, find the number of H atoms in this gas. Hence find the energy required to fully ionize all the H, in both electron volts and joules. How does this compare with average New Zealand household energy consumption? (d) Also find the amount of energy (in eV and J) required to fully ionize all the He (to give He++). Hence find the total energy required to ionize all the gas (in J). 3 (e) Compare the energy required for full ionization (from (d), in joules) with the thermal energy (in joules) in the gas at 106 K, given that each particle has thermal energy / kT. (Don't forget to include the thermal energy of all the free electrons as well as the positive ions.) From your answer, is it probable that this gas mixture is fully ionized at a temperature of one million kelvin?
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