Question

If the temperatures in the middle of the sun are 15 million K and those on the Earth are near 300 K, what is the relative ratio of the thermal speed of a hydrogen atom in the middle of the sun to that on the Earth? Assume that the mass of one hydrogen atom is 1.66*10^-27 kg.

What are the values of the actual thermal speeds (not the ratio) in that case?

How long would a hydrogen atom take to travel from the center of the sun to the Earth if it could escape the sun without any loss of energy during its journey?

Answer 1

The energy of a particle travelling with a velocity v is E = mv²/2

Equating this with the thermal energy in 3D = 3kT/2,

The thermal speed is given by

Uth = 3KT/m

The ratio for sun and earth is

= 3kTsun/m * /m/3kTearth = Tsun/Tearth Ucarth

um = V15 * 106/300 = V5* 104 = 223.606798 Ucarth

b)

The actual values are:

/m 3* 1.38 * 10-23 * 15 * 106 -= V37.4096 * 1010 = 1 .66 * 10-27 Usun = V 6.1163 * 10 m/s = V

Vearth = 36T/m=13 3* 1.38 * 10-23 * 300 1.66 * 10-27 = V748.1928 * 104 = 2735.3113m/s

c)

Atom does not lose energy means that velocity does not change.

time = distance/speed = (150*10⁶)/(6.1163*10⁵)=245.24631 seconds.