Calculate the rms speed of helium atoms near the surface of the sun at a temperature of about 6000K.

The average speed of particles in a gas is measured by root-mean square speed. The root-mean square speed depends on the molecule’s weight and temperature.

The expression to find the rms speed of helium atoms near the surface of the sun is as follows:

\({v_{rms}} = \sqrt {\frac{{3RT}}{M}} \)

Here, \({v_{{\rm{rms}}}}\)is the rms speed of helium atoms near the surface of the sun; \(R\)is the universal gas constant; \(T\)is the temperature; \(M\) is the mass of the helium atom.

Temperature, \(T = 6000\,{\rm{K}}\).

The rms speed of helium atom near the surface of the sun is calculated as follows:

\(\begin{aligned}{c}{v_{rms}} &= \sqrt {\frac{{3\left( {8.3145\,{{{\rm{kg}}{{\rm{m}}^{\rm{2}}}} \mathord{\left/

{\vphantom {{{\rm{kg}}{{\rm{m}}^{\rm{2}}}} {{{\rm{s}}^{\rm{2}}}}}} \right.

\kern-\nulldelimiterspace} {{{\rm{s}}^{\rm{2}}}}} \cdot {\rm{mo}}{{\rm{l}}^{{\rm{ - 1}}}} \cdot {{\rm{K}}^{{\rm{ - 1}}}}} \right)\left( {6000\,{\rm{K}}} \right)}}{{\left( {4\,{{\rm{g}} \mathord{\left/

{\vphantom {{\rm{g}} {{\rm{mol}}}}} \right.

\kern-\nulldelimiterspace} {{\rm{mol}}}}} \right)\left( {\frac{{{\rm{1}}{{\rm{0}}^{{\rm{ - 3}}}}\,{\rm{kg}}}}{{{\rm{1}}\,\,{\rm{g}}}}} \right)}}} \\ &= 6116.8\,\,{{\rm{m}} \mathord{\left/

{\vphantom {{\rm{m}} {\rm{s}}}} \right.

\kern-\nulldelimiterspace} {\rm{s}}}\end{aligned}\)

Hence, the rms speed of helium atom near the surface of the sun is \(6116.8\,\,{{\rm{m}} \mathord{\left/

{\vphantom {{\rm{m}} {\rm{s}}}} \right.

\kern-\nulldelimiterspace} {\rm{s}}}\).