Hydrogen on the Sun. ?The surface of the sun has a temperature of about 5800 K and consists largely of hydrogen atoms. (a) Find the rms speed of a hydrogen atom at this temperature. (The mass of a single hydrogen atom is 1.67 x 10? -27kg.) (b) The escape ½? speed for a particle to leave the gravitational influence of the sun is given by (2GM/R)? , where ?M ?is the sun’s mass, ?R its radius and ?G the gravitational constant (see Example 13.5 of Section 13.3). Use data in Appendix F to calculate this escape speed. (c) Can appreciable quantities of hydrogen escape from the sun? Can ?any ?hydrogen escape? Explain.

Solution 76P Step 1: 3kT The equation for rms speed, v rms = M Where, k = 1.38 × 10 -23kg m /s K (Boltzmann constant) T - Temperature of the gas M - Molar mass Step 2: a) rms speed of hydrogen atom can be calculated using the above equation. -27 Mass of hydrogen atom, M = 1.67 × 10 kg Temperature, T = 5800 K 23 2 2 Therefore, v rms = 3×1.38 × 10 kg m27 K ×5800 K 1.67 × 10 kg v = 14378 × 10 m /s 2 2 rms 4 vrms 11991 m/s = 1.2 × 10 m/s