Use the Saha Equation to determine the fraction of hydrogen atoms that are ioniz

Question

Use the Saha Equation to determine the fraction of hydrogen atoms that are ionized (N_II/N_total) at the center of the Sun. There the temperature is 15.7 million K and the number density of electrons is about n_e = 6.1 Times 10^31m^-3. Use Z_I=2, Z_II=1, and chi_I = 13.6 eV. Does your result agree with the fact that in reality, practically all of the hydrogen at the center of the Sun is ionized? If not, can you think of anything about the conditions near the center of the Sun that might result in more ionization than what you would normally calculate?

Explanation / Answer

Saha equation,

N(II)/Ntotal = (2Z(II)/ne.Z(I))[(2.pi.meKT)/h^2]^3/2.e(-X/KT)

me = mass of electron

h = planck's constant

K = Boltzman constant

Feed given values from above,

N(II)/Ntotal = (2 x 1/6.1 x 10^31 x 2)[(2 x 3.14 x 9.11 x 10^-31 x 1.38 x 10^-23 x 15.7 x 10^6)/(6.626 x 10^-34)^2]^3/2.e^(-2.18 x 10^-18/1.38 x 10^-23 x 15.7 x 10^6)

= 8.20 x 10^-33 x (2.82 x 10^21)^3/2.e^(-0.0101)

= 8.20 x 10^-33 x 1.50 x 10^32 x 0.99

= 1.22

Is the answer. It agrees with the fact that practically all of the hydrogen at the center of the sun in ionized.

Related Questions

Navigate

• Browse (All)
• Browse U
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.